| Title: | Analysis of Queueing Networks and Models |
|---|---|
| Description: | It provides versatile tools for analysis of birth and death based Markovian Queueing Models and Single and Multiclass Product-Form Queueing Networks. It implements M/M/1, M/M/c, M/M/Infinite, M/M/1/K, M/M/c/K, M/M/c/c, M/M/1/K/K, M/M/c/K/K, M/M/c/K/m, M/M/Infinite/K/K, Multiple Channel Open Jackson Networks, Multiple Channel Closed Jackson Networks, Single Channel Multiple Class Open Networks, Single Channel Multiple Class Closed Networks and Single Channel Multiple Class Mixed Networks. Also it provides a B-Erlang, C-Erlang and Engset calculators. This work is dedicated to the memory of D. Sixto Rios Insua. |
| Authors: | Pedro Canadilla |
| Maintainer: | Pedro Canadilla <[email protected]> |
| License: | GPL-2 |
| Version: | 0.2.12 |
| Built: | 2024-12-18 06:47:12 UTC |
| Source: | CRAN |
It provides a versatile tool for analysis of birth and death based Markovian Queueing Models and Single and Multiclass Product-Form Queueing Networks.
It implements the following basic markovian models:
| M/M/1, | M/M/c, | M/M/Infinite, | |
| M/M/1/K, | M/M/c/K, | M/M/c/c, | |
| M/M/1/K/K, | M/M/c/K/K, | M/M/c/K/m, | M/M/Infinite/K/K |
It also solves the following types of networks:
Multiple Channel Open Jackson Networks.
Multiple Channel Closed Jackson Networks.
Single Channel Multiple Class Open Networks.
Single Channel Multiple Class Closed Networks
Single Channel Multiple Class Mixed Networks
Also it provides B-Erlang, C-Erlang and Engset calculators.
This work is dedicated to the memory of D. Sixto Rios Insua.
All models are used in the same way:
Create inputs calling the appropiate NewInput.model. For example, x <- NewInput.MM1(lambda=0.25, mu=1, n=10) for a M/M/1 model. To know the exact acronymn model to use for NewInput function, you can search the html help or write help.search("NewInput") at the command line.
Optionally, as a help for creating the inputs, the CheckInput(x) function can be called
Solve the model calling y <- QueueingModel(x). In this step, the CheckInput(x) will be called. That is the reason that the previous step is optional
Finally, you can get a performance value as W(y), Wq(y) or a report of the principals performace values calling summary(y)
See the examples for more detailed information of the use.
Author, Maintainer and Copyright: Pedro Canadilla [email protected]
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## M/M/1 model summary(QueueingModel(NewInput.MM1(lambda=1/4, mu=1/3, n=0))) ## M/M/1/K model summary(QueueingModel(NewInput.MM1K(lambda=1/4, mu=1/3, k=3)))## M/M/1 model summary(QueueingModel(NewInput.MM1(lambda=1/4, mu=1/3, n=0))) ## M/M/1/K model summary(QueueingModel(NewInput.MM1K(lambda=1/4, mu=1/3, k=3)))
Returns the probability that all servers are busy
B_erlang(c=1, u=0)B_erlang(c=1, u=0)
c |
numbers of servers |
u |
lambda/mu, that is, ratio of rate of arrivals and rate of service |
Returns the probability that all servers are busy
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Jagerman1974] Jagerman, D. L. (1974).
Some properties of the Erlang loss function.
Bell System Tech. J. (53), 525-551
## two servers B_erlang(2, 0.5/0.7)## two servers B_erlang(2, 0.5/0.7)
Returns the probability to wait in queue because all servers are busy
C_erlang(c=1, r=0)C_erlang(c=1, r=0)
c |
numbers of servers |
r |
lambda/mu, that is, ratio of rate of arrivals and rate of service |
Returns the probability to wait in queue because all servers are busy
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## two servers C_erlang(2, 0.5/0.7)## two servers C_erlang(2, 0.5/0.7)
Generic S3 method to check the params of a queueing model (or network)
CheckInput(x, ...)CheckInput(x, ...)
x |
a object of class i_MM1, i_MMC, i_MM1K, i_MMCK, i_MM1KK, i_MMCKK, i_MMCC, i_MMCKM, i_MMInfKK, i_MMInf, i_OJN |
... |
aditional arguments |
Generic S3 method to check the params of a queueing model (or network)
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
CheckInput.i_MM1CheckInput.i_MMCCheckInput.i_MM1KCheckInput.i_MMCKCheckInput.i_MM1KKCheckInput.i_MMCKKCheckInput.i_MMCCCheckInput.i_MMCKMCheckInput.i_MMInfKKCheckInput.i_MMInfCheckInput.i_OJN
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Check the inputs CheckInput(i_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Check the inputs CheckInput(i_mm1)
Checks the input params of a generic Birth and Death process model
## S3 method for class 'i_BnD' CheckInput(x, ...)## S3 method for class 'i_BnD' CheckInput(x, ...)
x |
a object of class i_BnD |
... |
aditional arguments |
Checks the input params of a generic Birth and Death process model. The inputs params are created calling previously the NewInput.BnD
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Check the inputs CheckInput(i_BnD)## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Check the inputs CheckInput(i_BnD)
Check the input params of a Closed Jackson Network
## S3 method for class 'i_CJN' CheckInput(x, ...)## S3 method for class 'i_CJN' CheckInput(x, ...)
x |
a object of class i_CJN |
... |
aditional arguments |
Check the input params of a Closed Jackson Network. The inputs params are created calling previously the NewInput.CJN
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) CheckInput(cjn1)## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) CheckInput(cjn1)
Check the input params of a MultiClass Closed Network
## S3 method for class 'i_MCCN' CheckInput(x, ...)## S3 method for class 'i_MCCN' CheckInput(x, ...)
x |
a object of class i_MCCN |
... |
aditional arguments |
Check the input params of a MultiClass Closed Network. The inputs params are created calling previously the NewInput.MCCN
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) CheckInput(i_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) CheckInput(i_MCCN1)
Check the input params of a MultiClass Mixed Network
## S3 method for class 'i_MCMN' CheckInput(x, ...)## S3 method for class 'i_MCMN' CheckInput(x, ...)
x |
a object of class i_MCMN |
... |
aditional arguments |
Check the input params of a MultiClass Mixed Network. The inputs params are created calling previously the NewInput.MCMN
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) CheckInput(i_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) CheckInput(i_mcmn1)
Check the input params of a MultiClass Open Network
## S3 method for class 'i_MCON' CheckInput(x, ...)## S3 method for class 'i_MCON' CheckInput(x, ...)
x |
a object of class i_MCON |
... |
aditional arguments |
Check the input params of a MultiClass Open Network. The inputs params are created calling previously the NewInput.MCON
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) CheckInput(i_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) CheckInput(i_mcon1)
Checks the input params of a M/M/1 queueing model
## S3 method for class 'i_MM1' CheckInput(x, ...)## S3 method for class 'i_MM1' CheckInput(x, ...)
x |
a object of class i_MM1 |
... |
aditional arguments |
Checks the input params of a M/M/1 queueing model. The inputs params are created calling previously the NewInput.MM1
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Check the inputs CheckInput(i_mm1)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Check the inputs CheckInput(i_mm1)
Checks the input params of a M/M/1/K queueing model
## S3 method for class 'i_MM1K' CheckInput(x, ...)## S3 method for class 'i_MM1K' CheckInput(x, ...)
x |
a object of class i_MM1K |
... |
aditional arguments |
Checks the input params of a M/M/1/K queueing model. The inputs params are created calling previously the NewInput.MM1K
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## check the parameters CheckInput(i_mm1k)## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## check the parameters CheckInput(i_mm1k)
Checks the input params of a M/M/1/K/K queueing model
## S3 method for class 'i_MM1KK' CheckInput(x, ...)## S3 method for class 'i_MM1KK' CheckInput(x, ...)
x |
a object of class i_MM1KK |
... |
aditional arguments |
Checks the input params of a M/M/1/K/K queueing model. The inputs params are created calling previously the NewInput.MM1KK
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## check the parameters CheckInput(i_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## check the parameters CheckInput(i_mm1kk)
Checks the input params of a M/M/c queueing model
## S3 method for class 'i_MMC' CheckInput(x, ...)## S3 method for class 'i_MMC' CheckInput(x, ...)
x |
a object of class i_MMC |
... |
aditional arguments |
Checks the input params of a M/M/c queueing model. The inputs params are created calling previously the NewInput.MMC
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## check the parameters CheckInput(i_mmc)## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## check the parameters CheckInput(i_mmc)
Checks the input params of a M/M/c/c queueing model
## S3 method for class 'i_MMCC' CheckInput(x, ...)## S3 method for class 'i_MMCC' CheckInput(x, ...)
x |
a object of class i_MMCC |
... |
aditional arguments |
Checks the input params of a M/M/c/c queueing model. The inputs params are created calling previously the NewInput.MMCC
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## check the parameters CheckInput(i_mmcc)## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## check the parameters CheckInput(i_mmcc)
Checks the input params of a M/M/c/K queueing model
## S3 method for class 'i_MMCK' CheckInput(x, ...)## S3 method for class 'i_MMCK' CheckInput(x, ...)
x |
a object of class i_MMCK |
... |
aditional arguments |
Checks the input params of a M/M/c/K queueing model. The inputs params are created calling previously the NewInput.MMCK
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Check the inputs CheckInput(i_mmck)## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Check the inputs CheckInput(i_mmck)
Checks the input params of a M/M/c/K/K queueing model
## S3 method for class 'i_MMCKK' CheckInput(x, ...)## S3 method for class 'i_MMCKK' CheckInput(x, ...)
x |
a object of class i_MMCKK |
... |
aditional arguments |
Checks the input params of a M/M/c/K/K queueing model. The inputs params are created calling previously the NewInput.MMCKK
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## check the parameters CheckInput(i_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## check the parameters CheckInput(i_mmckk)
Checks the input params of a M/M/c/K/m queueing model
## S3 method for class 'i_MMCKM' CheckInput(x, ...)## S3 method for class 'i_MMCKM' CheckInput(x, ...)
x |
a object of class i_MMCKM |
... |
aditional arguments |
Checks the input params of a M/M/c/K/m queueing model. The inputs params are created calling previously the NewInput.MMCKM
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## check the parameters CheckInput(i_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## check the parameters CheckInput(i_mmckm)
Checks the input params of a M/M/Infinite queueing model
## S3 method for class 'i_MMInf' CheckInput(x, ...)## S3 method for class 'i_MMInf' CheckInput(x, ...)
x |
a object of class i_MMInf |
... |
aditional arguments |
Checks the input params of a M/M/Infinite queueing model. The inputs params are created calling previously the NewInput.MMInf
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Check the parameters CheckInput(i_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Check the parameters CheckInput(i_mminf)
Checks the input params of a M/M/Infinite/K/K queueing model
## S3 method for class 'i_MMInfKK' CheckInput(x, ...)## S3 method for class 'i_MMInfKK' CheckInput(x, ...)
x |
a object of class i_MMInfKK |
... |
aditional arguments |
Checks the input params of a M/M/Infinite/K/K queueing model. The inputs params are created calling previously the NewInput.MMInfKK
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## check the parameters CheckInput(i_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## check the parameters CheckInput(i_MMInfKK)
Check the input params of an Open Jackson Network
## S3 method for class 'i_OJN' CheckInput(x, ...)## S3 method for class 'i_OJN' CheckInput(x, ...)
x |
a object of class i_OJN |
... |
aditional arguments |
Check the input params of an Open Jackson Network. The inputs params are created calling previously the NewInput.OJN
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) ojn1 <- NewInput.OJN(prob, n1, n2, n3, n4) CheckInput(ojn1)## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) ojn1 <- NewInput.OJN(prob, n1, n2, n3, n4) CheckInput(ojn1)
Compare several queueing models in a tabulated format
CompareQueueingModels(model, ...) CompareQueueingModels2(models)CompareQueueingModels(model, ...) CompareQueueingModels2(models)
model |
A Queueing Model obtained calling QueueingModel from classes described in the details section |
... |
a separated by comma list of queueing models obtained calling QueueingModel from classes described in the details section |
models |
A list of queueing models obtained calling QueueingModel from classes described in the details section |
Compare several queueing models in a tabulated format. By now, only o_MM1, o_MMC, o_MMInf, o_MM1K, o_MMCK, o_MMCC, o_MM1KK, o_MMCKK, o_MMCKM, o_MMInfKK classes can be compared
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
q1 <- QueueingModel(NewInput.MM1(lambda=5, mu=7)) q2 <- QueueingModel(NewInput.MMC(lambda=5, mu=3, c=4)) q3 <- QueueingModel(NewInput.MMInf(lambda=3, mu=4)) q4 <- QueueingModel(NewInput.MMCC(lambda=5, mu=3, c=4)) CompareQueueingModels(q1, q2, q3) CompareQueueingModels2(list(q1, q2, q3, q4))q1 <- QueueingModel(NewInput.MM1(lambda=5, mu=7)) q2 <- QueueingModel(NewInput.MMC(lambda=5, mu=3, c=4)) q3 <- QueueingModel(NewInput.MMInf(lambda=3, mu=4)) q4 <- QueueingModel(NewInput.MMCC(lambda=5, mu=3, c=4)) CompareQueueingModels(q1, q2, q3) CompareQueueingModels2(list(q1, q2, q3, q4))
Returns the probability that all servers are busy
Engset(k=1, c=0, r=0)Engset(k=1, c=0, r=0)
k |
numbers of users |
c |
numbers of servers |
r |
lambda/mu, that is, ratio of rate of arrivals and rate of service |
Returns the probability of blocking in a finite source model
## three users, two servers Engset(3, 2, 0.5/0.7)## three users, two servers Engset(3, 2, 0.5/0.7)
Returns the inputs parameters of a already built queueing model (or network)
Inputs(x, ...)Inputs(x, ...)
x |
a object of class o_MM1, o_MMC, o_MM1K, o_MMCK, o_MM1KK, o_MMCKK, o_MMCC, o_MMCKM, o_MMInfKK, o_MMInf, o_OJN, o_MCON, o_MCCN, o_MCMN |
... |
aditional arguments |
Returns the input parameters of a queueing model (or network)
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
Inputs.o_MM1Inputs.o_MMCInputs.o_MM1KInputs.o_MMCKInputs.o_MM1KKInputs.o_MMCKKInputs.o_MMCCInputs.o_MMCKMInputs.o_MMInfKKInputs.o_MMInfInputs.o_OJNInputs.o_CJNInputs.o_MCONInputs.o_MCCNInputs.o_MCMN
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## It returns the Inputs Inputs(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## It returns the Inputs Inputs(o_mm1)
Returns the inputs parameters of a already built Birth and Death process model
## S3 method for class 'o_BnD' Inputs(x, ...)## S3 method for class 'o_BnD' Inputs(x, ...)
x |
a object of class o_BnD |
... |
aditional arguments |
Returns the input parameters of a generic Birth and Death process model. The inputs parameters are created calling previously the NewInput.BnD
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Build the model o_BnD <- QueueingModel(i_BnD) ## It returns the Inputs Inputs(o_BnD)## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Build the model o_BnD <- QueueingModel(i_BnD) ## It returns the Inputs Inputs(o_BnD)
Returns the input params of a Closed Jackson Network
## S3 method for class 'o_CJN' Inputs(x, ...)## S3 method for class 'o_CJN' Inputs(x, ...)
x |
a object of class o_CJN |
... |
aditional arguments |
Returns the input params of a Closed Jackson Network. The inputs parameters are created calling previously the NewInput.CJN
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Inputs(m_cjn1)## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Inputs(m_cjn1)
Returns the input params of a MultiClass Closed Network
## S3 method for class 'o_MCCN' Inputs(x, ...)## S3 method for class 'o_MCCN' Inputs(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Returns the input params of a MultiClass Closed Network. The inputs parameters are created calling previously the NewInput.MCCN
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Inputs(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Inputs(o_MCCN1)
Returns the input params of a MultiClass Mixed Network
## S3 method for class 'o_MCMN' Inputs(x, ...)## S3 method for class 'o_MCMN' Inputs(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Returns the input params of a MultiClass Mixed Network. The inputs parameters are created calling previously the NewInput.MCMN
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Inputs(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Inputs(o_mcmn1)
Returns the input params of a MultiClass Open Network
## S3 method for class 'o_MCON' Inputs(x, ...)## S3 method for class 'o_MCON' Inputs(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Returns the input params of a MultiClass Open Network. The inputs parameters are created calling previously the NewInput.MCON
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Inputs(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Inputs(o_mcon1)
Returns the inputs parameters of a already built M/M/1 queueing model
## S3 method for class 'o_MM1' Inputs(x, ...)## S3 method for class 'o_MM1' Inputs(x, ...)
x |
a object of class o_MM1 |
... |
aditional arguments |
Returns the input parameters of a M/M/1 queueing model. The inputs parameters are created calling previously the NewInput.MM1
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## It returns the Inputs Inputs(o_mm1)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## It returns the Inputs Inputs(o_mm1)
Returns the inputs parameters of a already built M/M/1/K queueing model
## S3 method for class 'o_MM1K' Inputs(x, ...)## S3 method for class 'o_MM1K' Inputs(x, ...)
x |
a object of class o_MM1K |
... |
aditional arguments |
Returns the input parameters of a M/M/1/K queueing model. The inputs parameters are created calling previously the NewInput.MM1K
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## It returns the Inputs Inputs(o_mm1k)## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## It returns the Inputs Inputs(o_mm1k)
Returns the inputs parameters of a already built M/M/1/K/K queueing model
## S3 method for class 'o_MM1KK' Inputs(x, ...)## S3 method for class 'o_MM1KK' Inputs(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Returns the input parameters of a M/M/1/K/K queueing model. The inputs parameters are created calling previously the NewInput.MM1KK
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## It returns the Inputs Inputs(o_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## It returns the Inputs Inputs(o_mm1kk)
Returns the inputs parameters of a already built M/M/c queueing model
## S3 method for class 'o_MMC' Inputs(x, ...)## S3 method for class 'o_MMC' Inputs(x, ...)
x |
a object of class o_MMC |
... |
aditional arguments |
Returns the input parameters of a M/M/c queueing model. The inputs parameters are created calling previously the NewInput.MMC
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## It returns the Inputs Inputs(o_mmc)## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## It returns the Inputs Inputs(o_mmc)
Returns the inputs parameters of a already built M/M/c/c queueing model
## S3 method for class 'o_MMCC' Inputs(x, ...)## S3 method for class 'o_MMCC' Inputs(x, ...)
x |
a object of class o_MMCC |
... |
aditional arguments |
Returns the input parameters of a M/M/c/c queueing model. The inputs parameters are created calling previously the NewInput.MMCC
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## It returns the Inputs Inputs(o_mmcc)## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## It returns the Inputs Inputs(o_mmcc)
Returns the inputs parameters of a already built M/M/c/K queueing model
## S3 method for class 'o_MMCK' Inputs(x, ...)## S3 method for class 'o_MMCK' Inputs(x, ...)
x |
a object of class o_MMCK |
... |
aditional arguments |
Returns the input parameters of a M/M/c/K queueing model. The inputs parameters are created calling previously the NewInput.MMCK
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## It returns the Inputs Inputs(o_mmck)## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## It returns the Inputs Inputs(o_mmck)
Returns the inputs parameters of a already built M/M/c/K/K queueing model
## S3 method for class 'o_MMCKK' Inputs(x, ...)## S3 method for class 'o_MMCKK' Inputs(x, ...)
x |
a object of class o_MMCKK |
... |
aditional arguments |
Returns the input parameters of a M/M/c/K/K queueing model. The inputs parameters are created calling previously the NewInput.MMCKK
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Retunns the Inputs Inputs(o_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Retunns the Inputs Inputs(o_mmckk)
Returns the inputs parameters of a already built M/M/c/K/m queueing model
## S3 method for class 'o_MMCKM' Inputs(x, ...)## S3 method for class 'o_MMCKM' Inputs(x, ...)
x |
a object of class o_MMCKM |
... |
aditional arguments |
Returns the input parameters of a M/M/c/K/m queueing model. The inputs parameters are created calling previously the NewInput.MMCKM
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## It returns the Inputs Inputs(o_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## It returns the Inputs Inputs(o_mmckm)
Returns the inputs parameters of a already built M/M/Infinite queueing model
## S3 method for class 'o_MMInf' Inputs(x, ...)## S3 method for class 'o_MMInf' Inputs(x, ...)
x |
a object of class o_MMInf |
... |
aditional arguments |
Returns the input parameters of a M/M/Infinite queueing model. The inputs parameters are created calling previously the NewInput.MMInf
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## It returns the Inputs Inputs(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## It returns the Inputs Inputs(o_mminf)
Returns the inputs parameters of a already built M/M/Infinite/K/K queueing model
## S3 method for class 'o_MMInfKK' Inputs(x, ...)## S3 method for class 'o_MMInfKK' Inputs(x, ...)
x |
a object of class o_MMInfKK |
... |
aditional arguments |
Returns the input parameters of a M/M/Infinite/K/K queueing model. The inputs parameters are created calling previously the NewInput.MMInfKK
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## It returns the Inputs Inputs(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## It returns the Inputs Inputs(o_MMInfKK)
Returns the input params of an Open Jackson Network
## S3 method for class 'o_OJN' Inputs(x, ...)## S3 method for class 'o_OJN' Inputs(x, ...)
x |
a object of class o_OJN |
... |
aditional arguments |
Returns the input params of an Open Jackson Network. The inputs parameters are created calling previously the NewInput.OJN
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) i_ojn1 <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the model o_ojn1 <- QueueingModel(i_ojn1) Inputs(o_ojn1)## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) i_ojn1 <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the model o_ojn1 <- QueueingModel(i_ojn1) Inputs(o_ojn1)
Returns the mean number of customers in a queueing model (or network)
L(x, ...)L(x, ...)
x |
a object of class o_MM1, o_MMC, o_MM1K, o_MMCK, o_MM1KK, o_MMCKK, o_MMCC, o_MMCKM, o_MMInfKK, o_MMInf, o_OJN, o_MCON, o_MCCN, o_MCMN |
... |
aditional arguments |
Returns the mean number of customers in a queueing model (or network)
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
L.o_MM1L.o_MMCL.o_MM1KL.o_MMCKL.o_MM1KKL.o_MMCKKL.o_MMCCL.o_MMCKML.o_MMInfKKL.o_MMInfL.o_OJNL.o_CJNL.o_MCONL.o_MCCNL.o_MCMN
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the L L(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the L L(o_mm1)
Returns the mean number of customers in the generic Birth and Death process model
## S3 method for class 'o_BnD' L(x, ...)## S3 method for class 'o_BnD' L(x, ...)
x |
a object of class o_BnD |
... |
aditional arguments |
Returns the mean number of customers in the generic Birth and Death process model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Build the model o_BnD <- QueueingModel(i_BnD) ## Returns the L L(o_BnD)## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Build the model o_BnD <- QueueingModel(i_BnD) ## Returns the L L(o_BnD)
Returns the mean number of customers of a Closed Jackson Network
## S3 method for class 'o_CJN' L(x, ...)## S3 method for class 'o_CJN' L(x, ...)
x |
a object of class o_CJN |
... |
aditional arguments |
Returns the mean number of customers of a Closed Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) L(m_cjn1)## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) L(m_cjn1)
Returns the mean number of customers of a MultiClass Closed Network
## S3 method for class 'o_MCCN' L(x, ...)## S3 method for class 'o_MCCN' L(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Returns the mean number of customers of a MultiClass Closed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) L(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) L(o_MCCN1)
Returns the mean number of customers of a MultiClass Mixed Network
## S3 method for class 'o_MCMN' L(x, ...)## S3 method for class 'o_MCMN' L(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Returns the mean number of customers of a MultiClass Mixed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) L(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) L(o_mcmn1)
Returns the mean number of customers of a MultiClass Open Network
## S3 method for class 'o_MCON' L(x, ...)## S3 method for class 'o_MCON' L(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Returns the mean number of customers of a MultiClass Open Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) L(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) L(o_mcon1)
Returns the mean number of customers in the M/M/1 queueing model
## S3 method for class 'o_MM1' L(x, ...)## S3 method for class 'o_MM1' L(x, ...)
x |
a object of class o_MM1 |
... |
aditional arguments |
Returns the mean number of customers in the M/M/1 queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the L L(o_mm1)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the L L(o_mm1)
Returns the mean number of customers in the M/M/1/K queueing model
## S3 method for class 'o_MM1K' L(x, ...)## S3 method for class 'o_MM1K' L(x, ...)
x |
a object of class o_MM1K |
... |
aditional arguments |
Returns the mean number of customers in the M/M/1/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the L L(o_mm1k)## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the L L(o_mm1k)
Returns the mean number of customers in the M/M/1/K/K queueing model
## S3 method for class 'o_MM1KK' L(x, ...)## S3 method for class 'o_MM1KK' L(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Returns the mean number of customers in the M/M/1/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the L L(o_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the L L(o_mm1kk)
Returns the mean number of customers in the M/M/c queueing model
## S3 method for class 'o_MMC' L(x, ...)## S3 method for class 'o_MMC' L(x, ...)
x |
a object of class o_MMC |
... |
aditional arguments |
Returns the mean number of customers in the M/M/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the L L(o_mmc)## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the L L(o_mmc)
Returns the mean number of customers in the M/M/c/c queueing model
## S3 method for class 'o_MMCC' L(x, ...)## S3 method for class 'o_MMCC' L(x, ...)
x |
a object of class o_MMCC |
... |
aditional arguments |
Returns the mean number of customers in the M/M/c/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the L L(o_mmcc)## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the L L(o_mmcc)
Returns the mean number of customers in the M/M/c/K queueing model
## S3 method for class 'o_MMCK' L(x, ...)## S3 method for class 'o_MMCK' L(x, ...)
x |
a object of class o_MMCK |
... |
aditional arguments |
Returns the mean number of customers in the M/M/c/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the L L(o_mmck)## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the L L(o_mmck)
Returns the mean number of customers in the M/M/c/K/K queueing model
## S3 method for class 'o_MMCKK' L(x, ...)## S3 method for class 'o_MMCKK' L(x, ...)
x |
a object of class o_MMCKK |
... |
aditional arguments |
Returns the mean number of customers in the M/M/c/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the L L(o_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the L L(o_mmckk)
Returns the mean number of customers in the M/M/c/K/m queueing model
## S3 method for class 'o_MMCKM' L(x, ...)## S3 method for class 'o_MMCKM' L(x, ...)
x |
a object of class o_MMCKM |
... |
aditional arguments |
Returns the mean number of customers in the M/M/c/K/m queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the L L(o_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the L L(o_mmckm)
Returns the mean number of customers in the M/M/Infinite queueing model
## S3 method for class 'o_MMInf' L(x, ...)## S3 method for class 'o_MMInf' L(x, ...)
x |
a object of class o_MMInf |
... |
aditional arguments |
Returns the mean number of customers in the M/M/Infinite queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the L L(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the L L(o_mminf)
Returns the mean number of customers in the M/M/Infinite/K/K queueing model
## S3 method for class 'o_MMInfKK' L(x, ...)## S3 method for class 'o_MMInfKK' L(x, ...)
x |
a object of class o_MMInfKK |
... |
aditional arguments |
Returns the mean number of customers in the M/M/Infinite/K/K queueing model
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the L L(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the L L(o_MMInfKK)
Returns the mean number of customers of an Open Jackson Network
## S3 method for class 'o_OJN' L(x, ...)## S3 method for class 'o_OJN' L(x, ...)
x |
a object of class o_OJN |
... |
aditional arguments |
Returns the mean number of customers of an Open Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the model o_ojn <- QueueingModel(i_ojn) L(o_ojn)## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the model o_ojn <- QueueingModel(i_ojn) L(o_ojn)
Returns the vector with the mean number of customers of each class in a multiclass queueing network
Lc(x, ...)Lc(x, ...)
x |
a object of class o_MCON, o_MCCN, o_MCMN |
... |
aditional arguments |
Returns the vector with the mean number of customers of each class in a multiclass queueing network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Lc(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Lc(o_mcon1)
Returns the vector with the mean number of customers of each class in a MultiClass Closed Network
## S3 method for class 'o_MCCN' Lc(x, ...)## S3 method for class 'o_MCCN' Lc(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Returns the vector with the mean number of customers of each class in a MultiClass Closed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Lc(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Lc(o_MCCN1)
Returns the vector with the mean number of customers of each class in a MultiClass Mixed Network
## S3 method for class 'o_MCMN' Lc(x, ...)## S3 method for class 'o_MCMN' Lc(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Returns the vector with the mean number of customers of each class in a MultiClass Mixed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Lc(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Lc(o_mcmn1)
Returns the vector with the mean number of customers of each class in a MultiClass Open Network
## S3 method for class 'o_MCON' Lc(x, ...)## S3 method for class 'o_MCON' Lc(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Returns the vector with the mean number of customers of each class in a MultiClass Open Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Lc(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Lc(o_mcon1)
Reports a matrix with the mean number of customers of class i in each node (server) j in a MultiClass Network
Lck(x, ...)Lck(x, ...)
x |
a object of class o_MCON, o_MCCN, o_MCMN |
... |
aditional arguments |
Reports a matrix with the mean number of customers of class i in each node (server) j in a MultiClass Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
Lck.o_MCONLck.o_MCCNLck.o_MCMN
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Lck(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Lck(o_mcon1)
Reports a matrix with the mean number of customers of class i in each node (server) j in a MultiClass Closed Network
## S3 method for class 'o_MCCN' Lck(x, ...)## S3 method for class 'o_MCCN' Lck(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Reports a matrix with the mean number of customers of class i in each node (server) j in a MultiClass Closed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Lck(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Lck(o_MCCN1)
Reports a matrix with the mean number of customers of class i in each node (server) j in a MultiClass Mixed Network
## S3 method for class 'o_MCMN' Lck(x, ...)## S3 method for class 'o_MCMN' Lck(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Reports a matrix with the mean number of customers of class i in each node (server) j in a MultiClass Mixed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Lck(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Lck(o_mcmn1)
Reports a matrix with the mean number of customers of class i in each node (server) j in a MultiClass Open Network
## S3 method for class 'o_MCON' Lck(x, ...)## S3 method for class 'o_MCON' Lck(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Reports a matrix with the mean number of customers of class i in each node (server) j in a MultiClass Open Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Lck(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Lck(o_mcon1)
Returns the vector with the mean number of customers in each node (server) of a queueing network
Lk(x, ...)Lk(x, ...)
x |
a object of class o_OJN, o_CJN, o_MCON, o_MCCN, o_MCMN |
... |
aditional arguments |
Returns the vector with the mean number of customers in each node (server) of a queueing network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
Lk.o_OJNLk.o_CJNLk.o_MCONLk.o_MCCNLk.o_MCMN
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Lk(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Lk(o_mcon1)
Returns the vector with the mean number of customers in each node (server) of a Closed Jackson Network
## S3 method for class 'o_CJN' Lk(x, ...)## S3 method for class 'o_CJN' Lk(x, ...)
x |
a object of class o_CJN |
... |
aditional arguments |
Returns the vector with the mean number of customers in each node (server) of a Closed Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Lk(m_cjn1)## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Lk(m_cjn1)
Returns a vector with the mean number of customers in each node (server) of a MultiClass Closed Network
## S3 method for class 'o_MCCN' Lk(x, ...)## S3 method for class 'o_MCCN' Lk(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Returns a vector with the mean number of customers in each node (server) of a MultiClass Closed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Lk(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Lk(o_MCCN1)
Returns a vector with the mean number of customers in each node (server) of a MultiClass Mixed Network
## S3 method for class 'o_MCMN' Lk(x, ...)## S3 method for class 'o_MCMN' Lk(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Returns a vector with the mean number of customers in each node (server) of a MultiClass Mixed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Lk(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Lk(o_mcmn1)
Returns a vector with the mean number of customers in each node (server) of a MultiClass Open Network
## S3 method for class 'o_MCON' Lk(x, ...)## S3 method for class 'o_MCON' Lk(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Returns a vector with the mean number of customers in each node (server) of a MultiClass Open Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Lk(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Lk(o_mcon1)
Returns the vector with the mean number of customers in each node (server) of an Open Jackson Network
## S3 method for class 'o_OJN' Lk(x, ...)## S3 method for class 'o_OJN' Lk(x, ...)
x |
a object of class o_OJN |
... |
aditional arguments |
Returns the vector with the mean number of customers in each node (server) of an Open Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the model o_ojn <- QueueingModel(i_ojn) Lk(o_ojn)## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the model o_ojn <- QueueingModel(i_ojn) Lk(o_ojn)
Returns the mean number of customers in the queue in a queueing model
Lq(x, ...)Lq(x, ...)
x |
a object of class o_MM1, o_MMC, o_MM1K, o_MMCK, o_MM1KK, o_MMCKK, o_MMCC, o_MMCKM, o_MMInfKK, o_MMInf |
... |
aditional arguments |
Returns the mean number of customers in the queue in a queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
Lq.o_MM1Lq.o_MMCLq.o_MM1KLq.o_MMCKLq.o_MM1KKLq.o_MMCKKLq.o_MMCCLq.o_MMCKMLq.o_MMInfKKLq.o_MMInf
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Lq Lq(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Lq Lq(o_mm1)
Returns the mean number of customers in the queue in the M/M/1 queueing model
## S3 method for class 'o_MM1' Lq(x, ...)## S3 method for class 'o_MM1' Lq(x, ...)
x |
a object of class o_MM1 |
... |
aditional arguments |
Returns the mean number of customers in the queue in the M/M/1 queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Lq Lq(o_mm1)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Lq Lq(o_mm1)
Returns the mean number of customers in the queue in the M/M/1/K queueing model
## S3 method for class 'o_MM1K' Lq(x, ...)## S3 method for class 'o_MM1K' Lq(x, ...)
x |
a object of class o_MM1K |
... |
aditional arguments |
Returns the mean number of customers in the queue in the M/M/1/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the Lq Lq(o_mm1k)## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the Lq Lq(o_mm1k)
Returns the mean number of customers in the queue in the M/M/1/K/K queueing model
## S3 method for class 'o_MM1KK' Lq(x, ...)## S3 method for class 'o_MM1KK' Lq(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Returns the mean number of customers in the queue in the M/M/1/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the Lq Lq(o_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the Lq Lq(o_mm1kk)
Returns the mean number of customers in the queue in the M/M/c queueing model
## S3 method for class 'o_MMC' Lq(x, ...)## S3 method for class 'o_MMC' Lq(x, ...)
x |
a object of class o_MMC |
... |
aditional arguments |
Returns the mean number of customers in the queue in the M/M/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the Lq Lq(o_mmc)## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the Lq Lq(o_mmc)
Returns the mean number of customers in the queue in the M/M/c/c queueing model
## S3 method for class 'o_MMCC' Lq(x, ...)## S3 method for class 'o_MMCC' Lq(x, ...)
x |
a object of class o_MMCC |
... |
aditional arguments |
Returns the mean number of customers in the queue in the M/M/c/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the Lq Lq(o_mmcc)## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the Lq Lq(o_mmcc)
Returns the mean number of customers in the queue in the M/M/c/K queueing model
## S3 method for class 'o_MMCK' Lq(x, ...)## S3 method for class 'o_MMCK' Lq(x, ...)
x |
a object of class o_MMCK |
... |
aditional arguments |
Returns the mean number of customers in the queue in the M/M/c/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the Lq Lq(o_mmck)## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the Lq Lq(o_mmck)
Returns the mean number of customers in the queue in the M/M/c/K/K queueing model
## S3 method for class 'o_MMCKK' Lq(x, ...)## S3 method for class 'o_MMCKK' Lq(x, ...)
x |
a object of class o_MMCKK |
... |
aditional arguments |
Returns the mean number of customers in the queue in the M/M/c/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the Lq Lq(o_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the Lq Lq(o_mmckk)
Returns the mean number of customers in the queue in the M/M/c/K/m queueing model
## S3 method for class 'o_MMCKM' Lq(x, ...)## S3 method for class 'o_MMCKM' Lq(x, ...)
x |
a object of class o_MMCKM |
... |
aditional arguments |
Returns the mean number of customers in the queue in the M/M/c/K/m queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the Lq Lq(o_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the Lq Lq(o_mmckm)
Returns the mean number of customers in the queue in the M/M/Infinite queueing model
## S3 method for class 'o_MMInf' Lq(x, ...)## S3 method for class 'o_MMInf' Lq(x, ...)
x |
a object of class o_MMInf |
... |
aditional arguments |
Returns the mean number of customers in the queue in the M/M/Infinite queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the Lq Lq(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the Lq Lq(o_mminf)
Returns the mean number of customers in the queue in the M/M/Infinite/K/K queueing model
## S3 method for class 'o_MMInfKK' Lq(x, ...)## S3 method for class 'o_MMInfKK' Lq(x, ...)
x |
a object of class o_MMInfKK |
... |
aditional arguments |
Returns the mean number of customers in the queue in the M/M/Infinite/K/K queueing model
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the Lq Lq(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the Lq Lq(o_MMInfKK)
Returns the mean number of customers in queue when there is queue in a queueing model
Lqq(x, ...)Lqq(x, ...)
x |
a object of class o_MM1, o_MMC, o_MM1K, o_MMCK, o_MM1KK, o_MMCKK, o_MMCC, o_MMCKM, o_MMInfKK, o_MMInf |
... |
aditional arguments |
Returns the mean number of customers in queue when there is queue in a queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
Lqq.o_MM1Lqq.o_MMCLqq.o_MM1KLqq.o_MMCKLqq.o_MM1KKLqq.o_MMCKKLqq.o_MMCCLqq.o_MMCKMLqq.o_MMInfKKLqq.o_MMInf
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Lqq Lqq(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Lqq Lqq(o_mm1)
Returns the mean number of customers in queue when there is queue in the M/M/1 queueing model
## S3 method for class 'o_MM1' Lqq(x, ...)## S3 method for class 'o_MM1' Lqq(x, ...)
x |
a object of class o_MM1 |
... |
aditional arguments |
Returns the mean number of customers in queue when there is queue in the M/M/1 queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Lqq Lqq(o_mm1)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Lqq Lqq(o_mm1)
Returns the mean number of customers in queue when there is queue in the M/M/1/K queueing model
## S3 method for class 'o_MM1K' Lqq(x, ...)## S3 method for class 'o_MM1K' Lqq(x, ...)
x |
a object of class o_MM1K |
... |
aditional arguments |
Returns the mean number of customers in queue when there is queue in the M/M/1/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the Lq Lqq(o_mm1k)## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the Lq Lqq(o_mm1k)
Returns the mean number of customers in queue when there is queue in the M/M/1/K/K queueing model
## S3 method for class 'o_MM1KK' Lqq(x, ...)## S3 method for class 'o_MM1KK' Lqq(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Returns the mean number of customers in queue when there is queue in the M/M/1/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the Lqq Lqq(o_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the Lqq Lqq(o_mm1kk)
Returns the mean number of customers in queue when there is queue in the M/M/c queueing model
## S3 method for class 'o_MMC' Lqq(x, ...)## S3 method for class 'o_MMC' Lqq(x, ...)
x |
a object of class o_MMC |
... |
aditional arguments |
Returns the mean number of customers in queue when there is queue in the M/M/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the Lqq Lqq(o_mmc)## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the Lqq Lqq(o_mmc)
Returns the mean number of customers in queue when there is queue in the M/M/c/c queueing model
## S3 method for class 'o_MMCC' Lqq(x, ...)## S3 method for class 'o_MMCC' Lqq(x, ...)
x |
a object of class o_MMCC |
... |
aditional arguments |
Returns the mean number of customers in queue when there is queue in the M/M/c/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the Lqq Lqq(o_mmcc)## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the Lqq Lqq(o_mmcc)
Returns the mean number of customers in queue when there is queue in the M/M/c/K queueing model
## S3 method for class 'o_MMCK' Lqq(x, ...)## S3 method for class 'o_MMCK' Lqq(x, ...)
x |
a object of class o_MMCK |
... |
aditional arguments |
Returns the mean number of customers in queue when there is queue in the M/M/c/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the Lqq Lqq(o_mmck)## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the Lqq Lqq(o_mmck)
Returns the mean number of customers in queue when there is queue in the M/M/c/K/K queueing model
## S3 method for class 'o_MMCKK' Lqq(x, ...)## S3 method for class 'o_MMCKK' Lqq(x, ...)
x |
a object of class o_MMCKK |
... |
aditional arguments |
Returns the mean number of customers in queue when there is queue in the M/M/c/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the Lqq Lqq(o_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the Lqq Lqq(o_mmckk)
Returns the mean number of customers in queue when there is queue in the M/M/c/K/m queueing model
## S3 method for class 'o_MMCKM' Lqq(x, ...)## S3 method for class 'o_MMCKM' Lqq(x, ...)
x |
a object of class o_MMCKM |
... |
aditional arguments |
Returns the mean number of customers in the queue in the M/M/c/K/m queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the Lqq Lqq(o_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the Lqq Lqq(o_mmckm)
Returns the mean number of customers in queue when there is queue in the M/M/Infinite queueing model
## S3 method for class 'o_MMInf' Lqq(x, ...)## S3 method for class 'o_MMInf' Lqq(x, ...)
x |
a object of class o_MMInf |
... |
aditional arguments |
Returns the mean number of customers in queue when there is queue in the M/M/Infinite queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the Lqq Lqq(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the Lqq Lqq(o_mminf)
Returns the mean number of customers in queue when there is queue in the M/M/Infinite/K/K queueing model
## S3 method for class 'o_MMInfKK' Lqq(x, ...)## S3 method for class 'o_MMInfKK' Lqq(x, ...)
x |
a object of class o_MMInfKK |
... |
aditional arguments |
Returns the mean number of customers in queue when there is queue in the M/M/Infinite/K/K queueing model
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the Lqq Lqq(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the Lqq Lqq(o_MMInfKK)
Define the inputs of a new generic Birth and Death process model
NewInput.BnD(lambda=NULL, mu=NULL)NewInput.BnD(lambda=NULL, mu=NULL)
lambda |
vectors of arrival rate depending of the number of users in the system. Observe that in R, the vectors starts counting at 1, so lambda[1] is the arrival rate when the system has 0 users on it |
mu |
vectors of service rate depending of the number of users in the system. Observe that in R, the vectors starts counting at 1, so mu[1] is the arrival rate when the system has 1 users on it |
Define the inputs of a new generic Birth and Death process model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu)## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu)
Define the inputs of a Closed Jackson Network
NewInput.CJN(prob=NULL, n=0, z=0, operational=FALSE, method=0, tol=0.001, ...) NewInput2.CJN(prob=NULL, n=0, z=0, operational=FALSE, method=0, tol=0.001, nodes) NewInput3.CJN(n, z, numNodes, vType, vVisit, vService, vChannel, method=0, tol=0.001)NewInput.CJN(prob=NULL, n=0, z=0, operational=FALSE, method=0, tol=0.001, ...) NewInput2.CJN(prob=NULL, n=0, z=0, operational=FALSE, method=0, tol=0.001, nodes) NewInput3.CJN(n, z, numNodes, vType, vVisit, vService, vChannel, method=0, tol=0.001)
prob |
It is probability transition matrix or visit ratio vector. That is, the prob[i, j] is the transition probability of node i to node j, or prob[i] is the visit ratio (a probability, that is, a value between 0 and 1) to node i. Also, the visit ratio can express the number of times that a client visits the queueing center, in a more operational point of view. See the parameter operational |
n |
number of customers in the Network |
z |
think time of the client |
operational |
If prob is a vector with the visit ratios, operational equal to FALSE gives to the visit ratio a probability meaning, that is, as the stacionary values of the imbedded markov chain. If operational is equal to TRUE, the operational point of view is used: it is the number of visits that the same client makes to a node. |
method |
If method is 0, the exact MVA algorith is used. If method is 1, the Bard-Schweitzer approximation algorithm is used. |
tol |
If the parameter method is 1, this is the tolerance parameter of the algorithm. |
... |
a separated by comma list of nodes of i_MM1, i_MMC or i_MMInf class |
nodes |
A list of nodes of i_MM1, i_MMC or i_MMInf class |
numNodes |
The number of nodes of the network |
vType |
A vector with the type of server: "Q" for a queueing node, "D" for a delay node |
vVisit |
A vector with the visit ratios. It represent visit counts to a center as if the parameter operational were TRUE |
vService |
A vector with the services time of each node |
vChannel |
A vector with the number of channels of the node. The type of the server has to be "Q" to be inspected |
Define the inputs of a Closed Jackson Network. For a operational use, NewInput3.CJN is recommended. For a more academic use, NewInput.CJN or NewInput2.CJN is recommended. Please, note that the different ways to create the inputs for a Closed Jackson Network are equivalent to each other, and no validation is done at this stage. The validation is done calling CheckInput function.
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) ## think time = 0 z <- 0 ## operational value operational <- FALSE ## definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) ## Not run: cjn1 <- NewInput2.CJN(prob, n, z, operational, 0, 0.001, list(n1, n2)) ## End(Not run) ## using visit ratios and service demands. See [Lazowska84] pag 117. ## E[S] cpu = 0.005, Visit cpu = 121, D cpu = E[S] cpu * Visit cpu = 0.605 cpu <- NewInput.MM1(mu=1/0.005) ## E[S] disk1 = 0.030, Visit disk1 = 70, D disk1 = E[S] disk1 * Visit disk1 = 2.1 disk1 <- NewInput.MM1(mu=1/0.030) ## E[S] disk2 = 0.027, Visit disk2 = 50, D disk2 = E[S] disk2 * Visit disk2 = 1.35 disk2 <- NewInput.MM1(mu=1/0.027) ## The visit ratios. vVisit <- c(121, 70, 50) operational <- TRUE net <- NewInput.CJN(prob=vVisit, n=3, z=15, operational, 0, 0.001, cpu, disk1, disk2) ## Using the operational creation function n <- 3 think <- 15 numNodes <- 3 vType <- c("Q", "Q", "Q") vService <- c(0.005, 0.030, 0.027) vChannel <- c(1, 1, 1) net2 <- NewInput3.CJN(n, think, numNodes, vType, vVisit, vService, vChannel, method=0, tol=0.001)## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) ## think time = 0 z <- 0 ## operational value operational <- FALSE ## definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) ## Not run: cjn1 <- NewInput2.CJN(prob, n, z, operational, 0, 0.001, list(n1, n2)) ## End(Not run) ## using visit ratios and service demands. See [Lazowska84] pag 117. ## E[S] cpu = 0.005, Visit cpu = 121, D cpu = E[S] cpu * Visit cpu = 0.605 cpu <- NewInput.MM1(mu=1/0.005) ## E[S] disk1 = 0.030, Visit disk1 = 70, D disk1 = E[S] disk1 * Visit disk1 = 2.1 disk1 <- NewInput.MM1(mu=1/0.030) ## E[S] disk2 = 0.027, Visit disk2 = 50, D disk2 = E[S] disk2 * Visit disk2 = 1.35 disk2 <- NewInput.MM1(mu=1/0.027) ## The visit ratios. vVisit <- c(121, 70, 50) operational <- TRUE net <- NewInput.CJN(prob=vVisit, n=3, z=15, operational, 0, 0.001, cpu, disk1, disk2) ## Using the operational creation function n <- 3 think <- 15 numNodes <- 3 vType <- c("Q", "Q", "Q") vService <- c(0.005, 0.030, 0.027) vChannel <- c(1, 1, 1) net2 <- NewInput3.CJN(n, think, numNodes, vType, vVisit, vService, vChannel, method=0, tol=0.001)
Define the inputs of a MultiClass Closed Network
NewInput.MCCN( classes, vNumber, vThink, nodes, vType, vVisit, vService, method=1, tol=0.01 )NewInput.MCCN( classes, vNumber, vThink, nodes, vType, vVisit, vService, method=1, tol=0.01 )
classes |
The number of classes |
vNumber |
A vector with the number of customers of each class |
vThink |
A vector with the think time of each class |
nodes |
The number of nodes in the network |
vType |
A vector with the type of node: "Q" for queueing nodes or "D" for delay nodes |
vVisit |
A matrix[i, j]. The rows represents the different visit count for each class i to each node j |
vService |
A matrix[i, j]. The rows represents the different service time for each class i in each node j |
method |
If method is 0, the exact MVA algorith is used. If method is 1, the Bard-Schweitzer approximation algorithm is used |
tol |
If the parameter method is 1, this is the tolerance parameter of the algorithm |
Define the inputs of a MultiClass Closed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService)
Define the inputs of a MultiClass Mixed Network
NewInput.MCMN( classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService, method=0, tol=0.01 )NewInput.MCMN( classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService, method=0, tol=0.01 )
classes |
The number of classes |
vLambda |
It is a vector with the rate of arrivals of each class |
vNumber |
A vector with the number of customers of each class |
vThink |
A vector with the think time of each class |
nodes |
The number of nodes in the network |
vType |
A vector with the type of node: "Q" for queueing nodes or "D" for delay nodes |
vVisit |
A matrix[i, j]. The rows represents the different visit count for each class i to each node j. Take caution about the orden: open classes are defined first and closed clasess are defined second |
vService |
A matrix[i, j]. The rows represents the different service times for each class i in each node j. Take caution about the orden: open classes are defined first and closed clasess are defined second. |
method |
If method is 0, the exact MVA algorith is used. If method is 1, the Bard-Schweitzer approximation algorithm is used |
tol |
If the parameter method is 1, this is the tolerance parameter of the algorithm |
Define the inputs of a MultiClass Mixed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 # A and B are open classes and C and D are closed classes. vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") # When the visit ratios and vService are set, # be sure that the open classes are in the first positions # and the closed classes after the open classes. vVisit <- matrix(data=1, nrow=4, ncol=2) # A and B are open clasess: # with demand service of 1/4 and 1/2 at the node 1 and 1/2 and 1 at the node 2 # C and D are open clasess: # with demand service of 1/4 and 1/2 at the node 1 and 1/2 and 1 at the node 2 vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 # A and B are open classes and C and D are closed classes. vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") # When the visit ratios and vService are set, # be sure that the open classes are in the first positions # and the closed classes after the open classes. vVisit <- matrix(data=1, nrow=4, ncol=2) # A and B are open clasess: # with demand service of 1/4 and 1/2 at the node 1 and 1/2 and 1 at the node 2 # C and D are open clasess: # with demand service of 1/4 and 1/2 at the node 1 and 1/2 and 1 at the node 2 vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService)
Define the inputs of a MultiClass Open Network
NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService)NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService)
classes |
The number of classes |
vLambda |
It is a vector with the rate of arrivals of each class |
nodes |
The number of nodes in the network |
vType |
A vector with the type of node: "Q" for queueing nodes or "D" for delay nodes |
vVisit |
A matrix[i, j]. The rows represents the different visit count for each class i to each node j |
vService |
A matrix[i, j]. The rows represents the different service times for each class i in each node j |
Define the inputs of a MultiClass Open Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService)
Define the inputs of a new M/M/1 queueing model
NewInput.MM1(lambda=0, mu=0, n=0)NewInput.MM1(lambda=0, mu=0, n=0)
lambda |
arrival rate |
mu |
server service rate |
n |
number of customers in the system from which you want to obtain its probabilities. Put n=0 for a idle probability (no customer present in the system or system idle). With n=-1, no probabilities are computed |
Define the inputs of a new M/M/1 queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0)
Define the inputs of a new M/M/1/K queueing model
NewInput.MM1K(lambda=0, mu=0, k=1)NewInput.MM1K(lambda=0, mu=0, k=1)
lambda |
arrival rate |
mu |
server service rate |
k |
system capacity |
Define the inputs of a new M/M/1/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15)## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15)
Define the inputs of a new M/M/1/K/K queueing model
NewInput.MM1KK(lambda=0, mu=0, k=1, method=3)NewInput.MM1KK(lambda=0, mu=0, k=1, method=3)
lambda |
arrival rate |
mu |
server service rate |
k |
system capacity |
method |
method of computation of the probabilities of k (system capacity) customers down. With method=0, the exact results are calculated using the formal definition. With method=1, aproximate results are calculated using Stirling aproximation of factorials and logaritms. With method=2, Jain's Method [Jain2007], pag. 26 is used. With method=3, the result that K-n customers up has a truncated poisson distribution is used [Kobayashi2012] pag. 709 |
Define the inputs of a new M/M/1/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Jain2007] Joti Lal Jain, Sri Gopal Mohanty, Walter Bohm (2007).
A course on Queueing Models.
Chapman-Hall.
[Kobayashi2012] Hisashi Kobayashi, Brian L. Mark, William Turin (2012).
Probability, Random Processes, and Statistical Analysis: Applications to Communications, Signal Processing, Queueing Theory and Mathematical Finance.
Cambridge University Press.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3)
Define the inputs of a new M/M/c queueing model
NewInput.MMC(lambda=0, mu=0, c=1, n=0, method=0)NewInput.MMC(lambda=0, mu=0, c=1, n=0, method=0)
lambda |
arrival rate |
mu |
server service rate |
c |
number of servers |
n |
number of customers in the system from which you want to obtain its probabilities. Put n=0 for a idle probability (no customer present in the system or system idle). With n=-1, no probabilities are computed |
method |
method of computation of the probabilities of n number of customers in the system. With method=0, the exact results are calculated using the formal definition. With method=1, aproximate results are calculated using Stirling aproximation of factorials and logaritms. |
Define the inputs of a new M/M/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0)## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0)
Define the inputs of a new M/M/c/c queueing model
NewInput.MMCC(lambda=0, mu=0, c=1, method=1)NewInput.MMCC(lambda=0, mu=0, c=1, method=1)
lambda |
arrival rate |
mu |
server service rate |
c |
number of servers |
method |
with method = 0, the state probabilities are calculated using the formal definition (with overflow problems with factorials; with method = 1 (default), the truncated poisson distribution is used (recomended for professional use) |
Define the inputs of a new M/M/c/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Kobayashi2012] Hisashi Kobayashi, Brian L. Mark, William Turin (2012).
Probability, Random Processes, and Statistical Analysis: Applications to Communications, Signal Processing, Queueing Theory and Mathematical Finance.
Cambridge University Press.
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15)## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15)
Define the inputs of a new M/M/c/K queueing model
NewInput.MMCK(lambda=0, mu=0, c=1, k=1)NewInput.MMCK(lambda=0, mu=0, c=1, k=1)
lambda |
arrival rate |
mu |
server service rate |
c |
number of servers |
k |
system capacity |
Define the inputs of a new M/M/c/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12)## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12)
Define the inputs of a new M/M/c/K/K queueing model
NewInput.MMCKK(lambda=0, mu=0, c=1, k=1, method=0)NewInput.MMCKK(lambda=0, mu=0, c=1, k=1, method=0)
lambda |
arrival rate |
mu |
server service rate |
c |
number of servers |
k |
system capacity |
method |
method of computation of the probabilities of k (system capacity) customers down. With method=0, the exact results are calculated using the formal definition. With method=1, aproximate results are calculated using Stirling aproximation of factorials and logaritms. With method=2, Jain's Method [Jain2007], pag. 26 is used |
Define the inputs of a new M/M/c/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Jain2007] Joti Lal Jain, Sri Gopal Mohanty, Walter Bohm (2007).
A course on Queueing Models.
Chapman-Hall.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0)
Define the inputs of a new M/M/c/K/m queueing model
NewInput.MMCKM(lambda=0, mu=0, c=1, k=1, m=1, method=0)NewInput.MMCKM(lambda=0, mu=0, c=1, k=1, m=1, method=0)
lambda |
arrival rate |
mu |
server service rate |
c |
number of servers |
k |
system capacity |
m |
poblation size. Please, observe that should be m >= k |
method |
method of computation of the probabilities of k (system capacity) customers down. With method=0, the exact results are calculated using the formal definition. With method=1, aproximate results are calculated using Stirling aproximation of factorials and logaritms. |
Define the inputs of a new M/M/c/K/m queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0)
Define the inputs of a new M/M/Infinite queueing model
NewInput.MMInf(lambda=0, mu=0, n=0)NewInput.MMInf(lambda=0, mu=0, n=0)
lambda |
arrival rate |
mu |
server service rate |
n |
number of customers in the system from which you want to obtain its probabilities. Put n=0 for a idle probability (no customer present in the system or system idle). With n=-1, no probabilities are computed |
Define the inputs of a new M/M/Infinite queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0)
Define the inputs of a new M/M/Infinite/K/K queueing model
NewInput.MMInfKK(lambda=0, mu=0, k=1)NewInput.MMInfKK(lambda=0, mu=0, k=1)
lambda |
arrival rate |
mu |
server service rate |
k |
system capacity |
Define the inputs of a new M/M/Infinite/K/K queueing model
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4)
Define the inputs of an Open Jackson Network
NewInput.OJN(prob=NULL, ...) NewInput2.OJN(prob=NULL, nodes) NewInput3.OJN(vLambda, numNodes, vType, vVisit, vService, vChannel)NewInput.OJN(prob=NULL, ...) NewInput2.OJN(prob=NULL, nodes) NewInput3.OJN(vLambda, numNodes, vType, vVisit, vService, vChannel)
prob |
It is probability transition matrix or visit ratio vector. That is, the prob[i, j] is the transition probability of node i to node j, or prob[i] is the visit ratio to node i (the visit ratio values doesn't need to be probabilities, that is, a value greater than 1 can be used here. See the examples) |
... |
a separated by comma list of nodes of i_MM1, i_MMC or i_MMInf class |
nodes |
A list of nodes of i_MM1, i_MMC or i_MMInf class |
vLambda |
Vector with the arrivals rates to each node |
numNodes |
Number of nodes |
vType |
A vector with the type of server: "Q" for a queueing node, "D" for a delay node |
vVisit |
A vector with the visit ratios |
vService |
A vector with the services time of each node |
vChannel |
A vector with the number of channels of the node. The type of the server has to be "Q" to be inspected |
Define the inputs of an Open Jackson Network. For a operational use, NewInput3.OJN is recommended. For a more academic use, NewInput.OJN or NewInput2.OJN is recommended. Please, note that the different ways to create the inputs for a Open Jackson Network are equivalent to each other, and no validation is done at this stage. The validation is done calling CheckInput function.
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) ojn1 <- NewInput.OJN(prob, n1, n2, n3, n4) ## Using function NewInput2 ## Not run: ojn1 <- NewInput2.OJN(prob, list(n1, n2, n3, n4)) ## End(Not run) ## Using visit ratios. Values taken from [Lazowska84], pag. 113. ## E[S] cpu = 0.005, Visit cpu = 121, D cpu = E[S] cpu * Visit cpu = 0.605 cpu <- NewInput.MM1(lambda=0.2, mu=1/0.005) ## E[S] disk1 = 0.030, Visit disk1 = 70, D disk1 = E[S] disk1 * Visit disk1 = 2.1 disk1 <- NewInput.MM1(lambda=0.2, mu=1/0.030) ## E[S] disk2 = 0.027, Visit disk2 = 50, D disk2 = E[S] disk2 * Visit disk2 = 1.35 disk2 <- NewInput.MM1(lambda=0.2, mu=1/0.027) ## In this example, to have the throughput per node, the visit ratios has to be given in this form. ## Please, don't use in the closed Jackson Network visit <- c(121, 70, 50) net <- NewInput.OJN(visit, cpu, disk1, disk2) ## Using NewInput3 vLambda <- c(0.2, 0.2, 0.2) vService <- c(0.005, 0.030, 0.027) numNodes <- 3 vType <- c("Q", "Q", "Q") vChannel <- c(1, 1, 1) net2 <- NewInput3.OJN(vLambda, numNodes, vType, visit, vService, vChannel)## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) ojn1 <- NewInput.OJN(prob, n1, n2, n3, n4) ## Using function NewInput2 ## Not run: ojn1 <- NewInput2.OJN(prob, list(n1, n2, n3, n4)) ## End(Not run) ## Using visit ratios. Values taken from [Lazowska84], pag. 113. ## E[S] cpu = 0.005, Visit cpu = 121, D cpu = E[S] cpu * Visit cpu = 0.605 cpu <- NewInput.MM1(lambda=0.2, mu=1/0.005) ## E[S] disk1 = 0.030, Visit disk1 = 70, D disk1 = E[S] disk1 * Visit disk1 = 2.1 disk1 <- NewInput.MM1(lambda=0.2, mu=1/0.030) ## E[S] disk2 = 0.027, Visit disk2 = 50, D disk2 = E[S] disk2 * Visit disk2 = 1.35 disk2 <- NewInput.MM1(lambda=0.2, mu=1/0.027) ## In this example, to have the throughput per node, the visit ratios has to be given in this form. ## Please, don't use in the closed Jackson Network visit <- c(121, 70, 50) net <- NewInput.OJN(visit, cpu, disk1, disk2) ## Using NewInput3 vLambda <- c(0.2, 0.2, 0.2) vService <- c(0.005, 0.030, 0.027) numNodes <- 3 vType <- c("Q", "Q", "Q") vChannel <- c(1, 1, 1) net2 <- NewInput3.OJN(vLambda, numNodes, vType, visit, vService, vChannel)
Pn returns the probabilities that a queueing model (or network) has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers in it
Pn(x, ...) Qn(x, ...)Pn(x, ...) Qn(x, ...)
x |
For Pn, an object of class o_MM1, o_MMC, o_MM1K, o_MMCK, o_MM1KK, o_MMCKK, o_MMCC, o_MMCKM, o_MMInfKK, o_MMInf, o_OJN, o_BnD. For Qn, an object of class o_MM1, o_MMC, o_MM1K, o_MMCK, o_MM1KK, o_MMCKK, o_MMCC, o_MMCKM, o_MMInfKK, o_MMInf |
... |
aditional arguments |
Pn returns the system probabilities of a queueing model (or network). Qn returns the probability that an effective arrival see n customers in the system
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
Pn.o_MM1Qn.o_MM1Pn.o_MMCQn.o_MMCPn.o_MM1KQn.o_MM1KPn.o_MMCKQn.o_MMCKPn.o_MM1KKQn.o_MM1KKPn.o_MMCKKQn.o_MMCKKPn.o_MMCCQn.o_MMCCPn.o_MMCKMQn.o_MMCKMPn.o_MMInfKKQn.o_MMInfKKPn.o_MMInfQn.o_MMInfPn.o_OJNPn.o_BnD
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the probabilities Pn(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the probabilities Pn(o_mm1)
Pn returns the probabilities that a generic Birth and Death process model has n customers.
## S3 method for class 'o_BnD' Pn(x, ...)## S3 method for class 'o_BnD' Pn(x, ...)
x |
a object of class o_BnD |
... |
aditional arguments |
Pn returns the probabilities that a generic Birth and Death process model has n customers.
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Build the model o_BnD <- QueueingModel(i_BnD) ## Returns the probabilities Pn(o_BnD) ## Simulating M/M/1 lambda <- rep(1/4, 200) mu <- rep(1/3, 200) pn_bnd_mm1 <- Pn(QueueingModel(NewInput.BnD(lambda=lambda, mu=mu))) pn_mm1 <- Pn(QueueingModel(NewInput.MM1(lambda=1/4, mu=1/3, n=200))) ## Simulating M/M/2 lambda <- rep(5, 200) mu <- c(1*10, rep(2*10, 199)) pn_mmc <- Pn(QueueingModel(NewInput.MMC(lambda=5, mu=10, c=2, n=200, method=0))) pn_bnd_mmc <- Pn(QueueingModel(NewInput.BnD(lambda=lambda, mu=mu))) ## Simulating M/M/1/K/K lambda <- c(2*0.25, 0.25) mu <- rep(4, 2) pn_mm1kk <- Pn(QueueingModel(NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3))) pn_bnd <- Pn(QueueingModel(NewInput.BnD(lambda=lambda, mu=mu)))## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Build the model o_BnD <- QueueingModel(i_BnD) ## Returns the probabilities Pn(o_BnD) ## Simulating M/M/1 lambda <- rep(1/4, 200) mu <- rep(1/3, 200) pn_bnd_mm1 <- Pn(QueueingModel(NewInput.BnD(lambda=lambda, mu=mu))) pn_mm1 <- Pn(QueueingModel(NewInput.MM1(lambda=1/4, mu=1/3, n=200))) ## Simulating M/M/2 lambda <- rep(5, 200) mu <- c(1*10, rep(2*10, 199)) pn_mmc <- Pn(QueueingModel(NewInput.MMC(lambda=5, mu=10, c=2, n=200, method=0))) pn_bnd_mmc <- Pn(QueueingModel(NewInput.BnD(lambda=lambda, mu=mu))) ## Simulating M/M/1/K/K lambda <- c(2*0.25, 0.25) mu <- rep(4, 2) pn_mm1kk <- Pn(QueueingModel(NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3))) pn_bnd <- Pn(QueueingModel(NewInput.BnD(lambda=lambda, mu=mu)))
Pn returns the probabilities that a M/M/1 queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers in it.
## S3 method for class 'o_MM1' Pn(x, ...) ## S3 method for class 'o_MM1' Qn(x, ...)## S3 method for class 'o_MM1' Pn(x, ...) ## S3 method for class 'o_MM1' Qn(x, ...)
x |
a object of class o_MM1 |
... |
aditional arguments |
Pn returns the probabilities that a M/M/1 queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers. By the PASTA property, both probabilities has to be the same.
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the probabilities Pn(o_mm1) Qn(o_mm1)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the probabilities Pn(o_mm1) Qn(o_mm1)
Pn returns the probabilities that a M/M/1/K queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers in it.
## S3 method for class 'o_MM1K' Pn(x, ...) ## S3 method for class 'o_MM1K' Qn(x, ...)## S3 method for class 'o_MM1K' Pn(x, ...) ## S3 method for class 'o_MM1K' Qn(x, ...)
x |
a object of class o_MM1K |
... |
aditional arguments |
Pn returns the probabilities that a M/M/1/K queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers.
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the probabilities Pn(o_mm1k) Qn(o_mm1k)## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the probabilities Pn(o_mm1k) Qn(o_mm1k)
Pn eeturns the probabilities of a M/M/1/K/K queueing model Qn returns the probabilities that an arrival that enter the system see n customers in it.
## S3 method for class 'o_MM1KK' Pn(x, ...) ## S3 method for class 'o_MM1KK' Qn(x, ...)## S3 method for class 'o_MM1KK' Pn(x, ...) ## S3 method for class 'o_MM1KK' Qn(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Pn returns the probabilities that a M/M/1/K/K queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers.
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the probabilities Pn(o_mm1kk) Qn(o_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the probabilities Pn(o_mm1kk) Qn(o_mm1kk)
Pn returns the probabilities that a M/M/c queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers in it.
## S3 method for class 'o_MMC' Pn(x, ...) ## S3 method for class 'o_MMC' Qn(x, ...)## S3 method for class 'o_MMC' Pn(x, ...) ## S3 method for class 'o_MMC' Qn(x, ...)
x |
a object of class o_MMC |
... |
aditional arguments |
Pn returns the probabilities that a M/M/c queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers. By the PASTA property, both probabilities has to be the same.
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the probabilities Pn(o_mmc) Qn(o_mmc)## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the probabilities Pn(o_mmc) Qn(o_mmc)
Pn returns the probabilities that a M/M/c/c queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers in it.
## S3 method for class 'o_MMCC' Pn(x, ...) ## S3 method for class 'o_MMCC' Qn(x, ...)## S3 method for class 'o_MMCC' Pn(x, ...) ## S3 method for class 'o_MMCC' Qn(x, ...)
x |
a object of class o_MMCC |
... |
aditional arguments |
Pn returns the probabilities that a M/M/c/c queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers.
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the probabilities Pn(o_mmcc) Qn(o_mmcc)## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the probabilities Pn(o_mmcc) Qn(o_mmcc)
Pn returns the probabilities that a M/M/c/K queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers in it.
## S3 method for class 'o_MMCK' Pn(x, ...) ## S3 method for class 'o_MMCK' Qn(x, ...)## S3 method for class 'o_MMCK' Pn(x, ...) ## S3 method for class 'o_MMCK' Qn(x, ...)
x |
a object of class o_MMCK |
... |
aditional arguments |
Pn returns the probabilities that a M/M/c/K queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers.
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the probabilities Pn(o_mmck) Qn(o_mmck)## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the probabilities Pn(o_mmck) Qn(o_mmck)
Pn returns the probabilities that a M/M/c/K/K queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers in it.
## S3 method for class 'o_MMCKK' Pn(x, ...) ## S3 method for class 'o_MMCKK' Qn(x, ...)## S3 method for class 'o_MMCKK' Pn(x, ...) ## S3 method for class 'o_MMCKK' Qn(x, ...)
x |
a object of class o_MMCKK |
... |
aditional arguments |
Pn returns the probabilities that a M/M/c/K/K queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers.
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the parameters Pn(o_mmckk) Qn(o_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the parameters Pn(o_mmckk) Qn(o_mmckk)
Pn returns the probabilities that a M/M/c/K/m queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers in it.
## S3 method for class 'o_MMCKM' Pn(x, ...) ## S3 method for class 'o_MMCKM' Qn(x, ...)## S3 method for class 'o_MMCKM' Pn(x, ...) ## S3 method for class 'o_MMCKM' Qn(x, ...)
x |
a object of class o_MMCKM |
... |
aditional arguments |
Pn returns the probabilities that a M/M/c/K/m queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers.
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the probabilities Pn(o_mmckm) Qn(o_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the probabilities Pn(o_mmckm) Qn(o_mmckm)
Pn returns the probabilities that a M/M/Infinite queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers in it.
## S3 method for class 'o_MMInf' Pn(x, ...) ## S3 method for class 'o_MMInf' Qn(x, ...)## S3 method for class 'o_MMInf' Pn(x, ...) ## S3 method for class 'o_MMInf' Qn(x, ...)
x |
a object of class o_MMInf |
... |
aditional arguments |
Pn returns the probabilities that a M/M/Infinite queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers. By the PASTA property, both probabilities has to be the same.
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the probabilities Pn(o_mminf) Qn(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the probabilities Pn(o_mminf) Qn(o_mminf)
Pn returns the probabilities that a M/M/Infinite/K/K queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers in it.
## S3 method for class 'o_MMInfKK' Pn(x, ...) ## S3 method for class 'o_MMInfKK' Qn(x, ...)## S3 method for class 'o_MMInfKK' Pn(x, ...) ## S3 method for class 'o_MMInfKK' Qn(x, ...)
x |
a object of class o_MMInfKK |
... |
aditional arguments |
Pn returns the probabilities that a M/M/Infinite/K/K queueing model has n customers.
Qn returns the probabilities that an arrival that enter the system see n customers.
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the probabilities Pn(o_MMInfKK) Qn(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the probabilities Pn(o_MMInfKK) Qn(o_MMInfKK)
Returns vector of the probabilities of each node (server) of an Open Jackson Network
## S3 method for class 'o_OJN' Pn(x, ...)## S3 method for class 'o_OJN' Pn(x, ...)
x |
a object of class o_OJN |
... |
aditional arguments |
Returns vector of the probabilities of each node (server) of an Open Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) # Deinition of the new input i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the models o_ojn <- QueueingModel(i_ojn) Pn(o_ojn)## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) # Deinition of the new input i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the models o_ojn <- QueueingModel(i_ojn) Pn(o_ojn)
Summary of the results of a generic Birth and Death process model.
## S3 method for class 'summary.o_BnD' print(x, ...)## S3 method for class 'summary.o_BnD' print(x, ...)
x |
a object of class summary.o_BnD |
... |
aditional arguments |
Summaries a generic Birth and Death process model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Build the model o_BnD <- QueueingModel(i_BnD) ## Report the results print(summary(o_BnD))## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Build the model o_BnD <- QueueingModel(i_BnD) ## Report the results print(summary(o_BnD))
Summary of the results of a Closed Jackson Network
## S3 method for class 'summary.o_CJN' print(x, ...)## S3 method for class 'summary.o_CJN' print(x, ...)
x |
a object of class summary.o_CJN |
... |
aditional arguments |
Summaries a Closed Jackson Network model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) print(summary(m_cjn1))## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) print(summary(m_cjn1))
Summary of the results of a MultiClass Closed Network
## S3 method for class 'summary.o_MCCN' print(x, ...)## S3 method for class 'summary.o_MCCN' print(x, ...)
x |
a object of class summary.o_MCCN |
... |
aditional arguments |
Summaries a MultiClass Closed Network model
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) print(summary(o_MCCN1))## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) print(summary(o_MCCN1))
Summary of the results of a MultiClass Mixed Network
## S3 method for class 'summary.o_MCMN' print(x, ...)## S3 method for class 'summary.o_MCMN' print(x, ...)
x |
a object of class summary.o_MCMN |
... |
aditional arguments |
Summaries a MultiClass Mixed Network model
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) print(summary(o_mcmn1))## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) print(summary(o_mcmn1))
Summary of the results of a MultiClass Open Network
## S3 method for class 'summary.o_MCON' print(x, ...)## S3 method for class 'summary.o_MCON' print(x, ...)
x |
a object of class summary.o_MCON |
... |
aditional arguments |
Summaries a MultiClass Open Network model
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) print(summary(o_mcon1))## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) print(summary(o_mcon1))
Summary of the results of a M/M/1 queueing model.
## S3 method for class 'summary.o_MM1' print(x, ...)## S3 method for class 'summary.o_MM1' print(x, ...)
x |
a object of class summary.o_MM1 |
... |
aditional arguments |
Summaries a M/M/1 queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Report the results print(summary(o_mm1))## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Report the results print(summary(o_mm1))
Summary of the results of a M/M/1/K queueing model.
## S3 method for class 'summary.o_MM1K' print(x, ...)## S3 method for class 'summary.o_MM1K' print(x, ...)
x |
a object of class summary.o_MM1K |
... |
aditional arguments |
Summaries a M/M/1/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Report the results print(summary(o_mm1k))## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Report the results print(summary(o_mm1k))
Summary of the results of a M/M/1/K/K queueing model.
## S3 method for class 'summary.o_MM1KK' print(x, ...)## S3 method for class 'summary.o_MM1KK' print(x, ...)
x |
a object of class summary.o_MM1KK |
... |
aditional arguments |
Summaries a M/M/1/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Report the results print(summary(o_mm1kk))## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Report the results print(summary(o_mm1kk))
Summary of the results of a M/M/c queueing model.
## S3 method for class 'summary.o_MMC' print(x, ...)## S3 method for class 'summary.o_MMC' print(x, ...)
x |
a object of class summary.o_MMC |
... |
aditional arguments |
Summaries a M/M/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Report the results print(summary(o_mmc))## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Report the results print(summary(o_mmc))
Summary of the results of a M/M/c/c queueing model.
## S3 method for class 'summary.o_MMCC' print(x, ...)## S3 method for class 'summary.o_MMCC' print(x, ...)
x |
a object of class summary.o_MMCC |
... |
aditional arguments |
Summaries a M/M/c/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Report the results print(summary(o_mmcc))## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Report the results print(summary(o_mmcc))
Summary of the results of a M/M/c/K queueing model.
## S3 method for class 'summary.o_MMCK' print(x, ...)## S3 method for class 'summary.o_MMCK' print(x, ...)
x |
a object of class summary.o_MMCK |
... |
aditional arguments |
Summaries a M/M/c/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Report the results print(summary(o_mmck))## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Report the results print(summary(o_mmck))
Summary of the results of a M/M/c/K/K queueing model.
## S3 method for class 'summary.o_MMCKK' print(x, ...)## S3 method for class 'summary.o_MMCKK' print(x, ...)
x |
a object of class summary.o_MMCKK |
... |
aditional arguments |
Summaries a M/M/c/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Report the results print(summary(o_mmckk))## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Report the results print(summary(o_mmckk))
Summary of the results of a M/M/c/K/m queueing model.
## S3 method for class 'summary.o_MMCKM' print(x, ...)## S3 method for class 'summary.o_MMCKM' print(x, ...)
x |
a object of class summary.o_MMCKM |
... |
aditional arguments |
Summaries a M/M/c/K/m queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Report the results print(summary(o_mmckm))## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Report the results print(summary(o_mmckm))
Summary of the results of a M/M/Infinite queueing model.
## S3 method for class 'summary.o_MMInf' print(x, ...)## S3 method for class 'summary.o_MMInf' print(x, ...)
x |
a object of class summary.o_MMInf |
... |
aditional arguments |
Summaries a M/M/Infinite queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Report the results print(summary(o_mminf))## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Report the results print(summary(o_mminf))
Reports the results of a M/M/Infinite/K/K queueing model.
## S3 method for class 'summary.o_MMInfKK' print(x, ...)## S3 method for class 'summary.o_MMInfKK' print(x, ...)
x |
a object of class summary.o_MMInfKK |
... |
aditional arguments |
Summaries a M/M/Infinite/K/K queueing model
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Report the results print(summary(o_MMInfKK))## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Report the results print(summary(o_MMInfKK))
Reports the results of an Open Jackson Network
## S3 method for class 'summary.o_OJN' print(x, ...)## S3 method for class 'summary.o_OJN' print(x, ...)
x |
a object of class summary.o_OJN |
... |
aditional arguments |
Summaries an Open Jackson Network model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) o_ojn <- QueueingModel(i_ojn) print(summary(o_ojn))## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) o_ojn <- QueueingModel(i_ojn) print(summary(o_ojn))
Generic S3 method to build a queueing model (or network)
QueueingModel(x, ...)QueueingModel(x, ...)
x |
a object of class i_MM1, i_MMC, i_MM1K, i_MMCK, i_MM1KK, i_MMCKK, i_MMCC, i_MMCKM, i_MMInfKK, i_MMInf, i_OJN, i_MCON |
... |
aditional arguments |
Generic S3 method to build a queueing model (or network)
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
QueueingModel.i_MM1QueueingModel.i_MMCQueueingModel.i_MM1KQueueingModel.i_MMCKQueueingModel.i_MM1KKQueueingModel.i_MMCKKQueueingModel.i_MMCCQueueingModel.i_MMCKMQueueingModel.i_MMInfKKQueueingModel.i_MMInfQueueingModel.i_OJNQueueingModel.i_MCON
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model QueueingModel(i_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model QueueingModel(i_mm1)
Builds a a generic Birth and Death process model
## S3 method for class 'i_BnD' QueueingModel(x, ...)## S3 method for class 'i_BnD' QueueingModel(x, ...)
x |
a object of class i_BnD |
... |
aditional arguments |
Build a generic Birth and Death process model. It also checks the input params calling the CheckInput.i_BnD
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Build the model o_BnD <- QueueingModel(i_BnD)## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Build the model o_BnD <- QueueingModel(i_BnD)
Builds one Closed Jackson Network
## S3 method for class 'i_CJN' QueueingModel(x, ...)## S3 method for class 'i_CJN' QueueingModel(x, ...)
x |
a object of class i_CJN |
... |
aditional arguments |
Build one Closed Jackson Network. It also checks the input params calling the CheckInput.i_CJN
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) m_cjn1## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) m_cjn1
Builds one MultiClass Closed Network
## S3 method for class 'i_MCCN' QueueingModel(x, ...)## S3 method for class 'i_MCCN' QueueingModel(x, ...)
x |
a object of class i_MCCN |
... |
aditional arguments |
Build one MultiClass Closed Network. It also checks the input params calling the CheckInput.i_MCCN
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) o_MCCN1## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) o_MCCN1
Builds one MultiClass Mixed Network
## S3 method for class 'i_MCMN' QueueingModel(x, ...)## S3 method for class 'i_MCMN' QueueingModel(x, ...)
x |
a object of class i_MCMN |
... |
aditional arguments |
Build one MultiClass Mixed Network. It also checks the input params calling the CheckInput.i_MCMN
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) o_mcmn1## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) o_mcmn1
Builds one MultiClass Open Network
## S3 method for class 'i_MCON' QueueingModel(x, ...)## S3 method for class 'i_MCON' QueueingModel(x, ...)
x |
a object of class i_MCON |
... |
aditional arguments |
Build one MultiClass Open Network. It also checks the input params calling the CheckInput.i_MCON
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) o_mcon1## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) o_mcon1
Builds a M/M/1 queueing model
## S3 method for class 'i_MM1' QueueingModel(x, ...)## S3 method for class 'i_MM1' QueueingModel(x, ...)
x |
a object of class i_MM1 |
... |
aditional arguments |
Build a M/M/1 queueing model. It also checks the input params calling the CheckInput.i_MM1
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model QueueingModel(i_mm1)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model QueueingModel(i_mm1)
Builds a M/M/1/K queueing model
## S3 method for class 'i_MM1K' QueueingModel(x, ...)## S3 method for class 'i_MM1K' QueueingModel(x, ...)
x |
a object of class i_MM1K |
... |
aditional arguments |
Build a M/M/1/K queueing model. It also checks the input params calling the CheckInput.i_MM1K
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model QueueingModel(i_mm1k)## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model QueueingModel(i_mm1k)
Builds a M/M/1/K/K queueing model
## S3 method for class 'i_MM1KK' QueueingModel(x, ...)## S3 method for class 'i_MM1KK' QueueingModel(x, ...)
x |
a object of class i_MM1KK |
... |
aditional arguments |
Build a M/M/1/K/K queueing model. It also checks the input params calling the CheckInput.i_MM1KK
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model QueueingModel(i_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model QueueingModel(i_mm1kk)
Builds a M/M/c queueing model
## S3 method for class 'i_MMC' QueueingModel(x, ...)## S3 method for class 'i_MMC' QueueingModel(x, ...)
x |
a object of class i_MMC |
... |
aditional arguments |
Build a M/M/c/ queueing model. It also checks the input params calling the CheckInput.i_MMC
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model QueueingModel(i_mmc)## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model QueueingModel(i_mmc)
Builds a M/M/c/c queueing model
## S3 method for class 'i_MMCC' QueueingModel(x, ...)## S3 method for class 'i_MMCC' QueueingModel(x, ...)
x |
a object of class i_MMCC |
... |
aditional arguments |
Build a M/M/c/c queueing model. It also checks the input params calling the CheckInput.i_MMCC
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model QueueingModel(i_mmcc)## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model QueueingModel(i_mmcc)
Builds a M/M/c/K queueing model
## S3 method for class 'i_MMCK' QueueingModel(x, ...)## S3 method for class 'i_MMCK' QueueingModel(x, ...)
x |
a object of class i_MMCK |
... |
aditional arguments |
Build a M/M/c/K queueing model. It also checks the input params calling the CheckInput.i_MMCK
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model QueueingModel(i_mmck)## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model QueueingModel(i_mmck)
Builds a M/M/c/K/K queueing model
## S3 method for class 'i_MMCKK' QueueingModel(x, ...)## S3 method for class 'i_MMCKK' QueueingModel(x, ...)
x |
a object of class i_MMCKK |
... |
aditional arguments |
Build a M/M/c/K/K queueing model. It also checks the input params calling the CheckInput.i_MMCKK
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model QueueingModel(i_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model QueueingModel(i_mmckk)
Builds a M/M/c/K/m queueing model
## S3 method for class 'i_MMCKM' QueueingModel(x, ...)## S3 method for class 'i_MMCKM' QueueingModel(x, ...)
x |
a object of class i_MMCKM |
... |
aditional arguments |
Build a M/M/c/K/m queueing model. It also checks the input params calling the CheckInput.i_MMCKM
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model QueueingModel(i_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model QueueingModel(i_mmckm)
Builds a M/M/Infinite queue model
## S3 method for class 'i_MMInf' QueueingModel(x, ...)## S3 method for class 'i_MMInf' QueueingModel(x, ...)
x |
a object of class i_MMInf |
... |
aditional arguments |
Build a M/M/Infinite model. It also checks the input params calling the CheckInput.i_MMInf
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model QueueingModel(i_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model QueueingModel(i_mminf)
Builds a M/M/Infinite/K/K queueing model
## S3 method for class 'i_MMInfKK' QueueingModel(x, ...)## S3 method for class 'i_MMInfKK' QueueingModel(x, ...)
x |
a object of class i_MMInfKK |
... |
aditional arguments |
Build a M/M/Infinite/K/K queueing model. It also checks the input params calling the CheckInput.i_MMInfKK
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model QueueingModel(i_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model QueueingModel(i_MMInfKK)
Builds one Open Jackson Network
## S3 method for class 'i_OJN' QueueingModel(x, ...)## S3 method for class 'i_OJN' QueueingModel(x, ...)
x |
a object of class i_OJN |
... |
aditional arguments |
Build one Open Jackson Network. It also checks the input params calling the CheckInput.i_OJN
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) ojn1 <- NewInput.OJN(prob, n1, n2, n3, n4) m_ojn1 <- QueueingModel(ojn1) m_ojn1## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) ojn1 <- NewInput.OJN(prob, n1, n2, n3, n4) m_ojn1 <- QueueingModel(ojn1) m_ojn1
Reports the results of a queueing model.
Report(x, ...)Report(x, ...)
x |
i_MM1, i_MMC, i_MM1K, i_MMCK, i_MM1KK, i_MMCKK, i_MMCC, i_MMCKM, i_MMInfKK, i_MMInf, i_OJN, i_MCON |
... |
aditional arguments |
Generic S3 method to report a queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Report the results Report(o_mm1)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Report the results Report(o_mm1)
Reports the results of a M/M/1 queueing model.
## S3 method for class 'o_BnD' Report(x, ...)## S3 method for class 'o_BnD' Report(x, ...)
x |
a object of class o_BnD |
... |
aditional arguments |
Generates a report of the queueing model received as parameter
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Build the model o_BnD <- QueueingModel(i_BnD) ## Report the results Report(o_BnD)## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Build the model o_BnD <- QueueingModel(i_BnD) ## Report the results Report(o_BnD)
Reports the results of a Closed Jackson Network
## S3 method for class 'o_CJN' Report(x, ...)## S3 method for class 'o_CJN' Report(x, ...)
x |
a object of class o_CJN |
... |
aditional arguments |
Generates a report of the queueing network received as parameter
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Report(m_cjn1)## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Report(m_cjn1)
Reports the results of a MultiClass Closed Network
## S3 method for class 'o_MCCN' Report(x, ...)## S3 method for class 'o_MCCN' Report(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Generates a report of the queueing network received as parameter
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Report(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Report(o_MCCN1)
Reports the results of a MultiClass Mixed Network
## S3 method for class 'o_MCMN' Report(x, ...)## S3 method for class 'o_MCMN' Report(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Generates a report of the queueing network received as parameter
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Report(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Report(o_mcmn1)
Reports the results of a MultiClass Open Network
## S3 method for class 'o_MCON' Report(x, ...)## S3 method for class 'o_MCON' Report(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Generates a report of the queueing network received as parameter
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Report(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Report(o_mcon1)
Reports the results of a M/M/1 queueing model.
## S3 method for class 'o_MM1' Report(x, ...)## S3 method for class 'o_MM1' Report(x, ...)
x |
a object of class o_MM1 |
... |
aditional arguments |
Generates a report of the queueing model received as parameter
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Report the results Report(o_mm1)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Report the results Report(o_mm1)
Reports the results of a M/M/1/K queueing model.
## S3 method for class 'o_MM1K' Report(x, ...)## S3 method for class 'o_MM1K' Report(x, ...)
x |
a object of class o_MM1K |
... |
aditional arguments |
Generates a report of the queueing model received as parameter
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Report the results Report(o_mm1k)## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Report the results Report(o_mm1k)
Reports the results of a M/M/1/K/K queueing model.
## S3 method for class 'o_MM1KK' Report(x, ...)## S3 method for class 'o_MM1KK' Report(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Generates a report of the queueing model received as parameter
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Report the results Report(o_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Report the results Report(o_mm1kk)
Reports the results of a M/M/c queueing model.
## S3 method for class 'o_MMC' Report(x, ...)## S3 method for class 'o_MMC' Report(x, ...)
x |
a object of class o_MMC |
... |
aditional arguments |
Generates a report of the queueing model received as parameter
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Report the results Report(o_mmc)## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Report the results Report(o_mmc)
Reports the results of a M/M/c/c queueing model.
## S3 method for class 'o_MMCC' Report(x, ...)## S3 method for class 'o_MMCC' Report(x, ...)
x |
a object of class o_MMCC |
... |
aditional arguments |
Generates a report of the queueing model received as parameter
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Report the results Report(o_mmcc)## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Report the results Report(o_mmcc)
Reports the results of a M/M/c/K queueing model.
## S3 method for class 'o_MMCK' Report(x, ...)## S3 method for class 'o_MMCK' Report(x, ...)
x |
a object of class o_MMCK |
... |
aditional arguments |
Generates a report of the queueing model received as parameter
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Report the results Report(o_mmck)## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Report the results Report(o_mmck)
Reports the results of a M/M/c/K/K queueing model.
## S3 method for class 'o_MMCKK' Report(x, ...)## S3 method for class 'o_MMCKK' Report(x, ...)
x |
a object of class o_MMCKK |
... |
aditional arguments |
Generates a report of the queueing model received as parameter
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Report the results Report(o_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Report the results Report(o_mmckk)
Reports the results of a M/M/c/K/m queueing model.
## S3 method for class 'o_MMCKM' Report(x, ...)## S3 method for class 'o_MMCKM' Report(x, ...)
x |
a object of class o_MMCKM |
... |
aditional arguments |
Generates a report of the queueing model received as parameter
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Report the results Report(o_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Report the results Report(o_mmckm)
Reports the results of a M/M/Infinite queueing model.
## S3 method for class 'o_MMInf' Report(x, ...)## S3 method for class 'o_MMInf' Report(x, ...)
x |
a object of class o_MMInf |
... |
aditional arguments |
Generates a report of the queueing model received as parameter
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Report the results Report(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Report the results Report(o_mminf)
Reports the results of a M/M/Infinite/K/K queueing model.
## S3 method for class 'o_MMInfKK' Report(x, ...)## S3 method for class 'o_MMInfKK' Report(x, ...)
x |
a object of class o_MMInfKK |
... |
aditional arguments |
Generates a report of the queueing model received as parameter
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Report the results Report(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Report the results Report(o_MMInfKK)
Reports the results of an Open Jackson Network
## S3 method for class 'o_OJN' Report(x, ...)## S3 method for class 'o_OJN' Report(x, ...)
x |
a object of class o_OJN |
... |
aditional arguments |
Generates a report of the queueing network received as parameter
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) o_ojn <- QueueingModel(i_ojn) Report(o_ojn)## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) o_ojn <- QueueingModel(i_ojn) Report(o_ojn)
Reports the server use of a queueing model)
RO(x, ...)RO(x, ...)
x |
a object of class o_MM1, o_MMC, o_MM1K, o_MMCK, o_MM1KK, o_MMCKK, o_MMCC, o_MMCKM, o_MMInfKK, o_MMInf |
... |
aditional arguments |
Reports the server use of a queueing model (or network)
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
RO.o_MM1RO.o_MMCRO.o_MM1KRO.o_MMCKRO.o_MM1KKRO.o_MMCKKRO.o_MMCCRO.o_MMCKMRO.o_MMInfKKRO.o_MMInf
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Report the use of the server RO(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Report the use of the server RO(o_mm1)
Reports the server use of a M/M/1 queueing model
## S3 method for class 'o_MM1' RO(x, ...)## S3 method for class 'o_MM1' RO(x, ...)
x |
a object of class o_MM1 |
... |
aditional arguments |
Reports the server use of a M/M/1 queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Report the use of the server RO(o_mm1)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Report the use of the server RO(o_mm1)
Reports the server use of a M/M/1/K queueing model
## S3 method for class 'o_MM1K' RO(x, ...)## S3 method for class 'o_MM1K' RO(x, ...)
x |
a object of class o_MM1K |
... |
aditional arguments |
Reports the server use of a M/M/1/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Report the use of the server RO(o_mm1k)## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Report the use of the server RO(o_mm1k)
Reports the server use of a M/M/1/K/K queueing model
## S3 method for class 'o_MM1KK' RO(x, ...)## S3 method for class 'o_MM1KK' RO(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Reports the server use of a M/M/1/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Report the use of the server RO(o_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Report the use of the server RO(o_mm1kk)
Reports the server use of a M/M/c queueing model
## S3 method for class 'o_MMC' RO(x, ...)## S3 method for class 'o_MMC' RO(x, ...)
x |
a object of class o_MMC |
... |
aditional arguments |
Reports the server use of a M/M/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Report the use of the server RO(o_mmc)## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Report the use of the server RO(o_mmc)
Reports the server use of a M/M/c/c queueing model
## S3 method for class 'o_MMCC' RO(x, ...)## S3 method for class 'o_MMCC' RO(x, ...)
x |
a object of class o_MMCC |
... |
aditional arguments |
Reports the server use of a M/M/c/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Report the use of the server RO(o_mmcc)## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Report the use of the server RO(o_mmcc)
Reports the server use of a M/M/c/K queueing model
## S3 method for class 'o_MMCK' RO(x, ...)## S3 method for class 'o_MMCK' RO(x, ...)
x |
a object of class o_MMCK |
... |
aditional arguments |
Reports the server use of a M/M/c/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Report the use of the server RO(o_mmck)## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Report the use of the server RO(o_mmck)
Reports the server use of a M/M/c/K/K queueing model
## S3 method for class 'o_MMCKK' RO(x, ...)## S3 method for class 'o_MMCKK' RO(x, ...)
x |
a object of class o_MMCKK |
... |
aditional arguments |
Reports the server use of a M/M/c/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Report the use of the server RO(o_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Report the use of the server RO(o_mmckk)
Reports the server use of a M/M/c/K/m queueing model
## S3 method for class 'o_MMCKM' RO(x, ...)## S3 method for class 'o_MMCKM' RO(x, ...)
x |
a object of class o_MMCKM |
... |
aditional arguments |
Reports the server use of a M/M/c/K/m queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Report the use of the server RO(o_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Report the use of the server RO(o_mmckm)
Reports the server use of a M/M/Infinite queueing model
## S3 method for class 'o_MMInf' RO(x, ...)## S3 method for class 'o_MMInf' RO(x, ...)
x |
a object of class o_MMInf |
... |
aditional arguments |
Reports the server use of a M/M/Infinite queueing model. It should be noted that in this model, the RO parameter has a different meaning, its the traffic intensity and it coincides exactly with the average number of customers in the system (L)
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
QueueingModel.i_MMInfL.o_MMInf
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Report the use of the server RO(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Report the use of the server RO(o_mminf)
Reports the server use of a M/M/Infinite/K/K queueing model
## S3 method for class 'o_MMInfKK' RO(x, ...)## S3 method for class 'o_MMInfKK' RO(x, ...)
x |
a object of class o_MMInfKK |
... |
aditional arguments |
Reports the server use of a M/M/Infinite/K/K queueing model
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Report the use of the server RO(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Report the use of the server RO(o_MMInfKK)
Reports a matrix with the use of class i in each node (server) j in a MultiClass Queueing Network
ROck(x, ...)ROck(x, ...)
x |
a object of class o_MCON, o_MCCN, o_MCMN |
... |
aditional arguments |
Reports a matrix with the use of class i in each node (server) j in a MultiClass Queueing Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos CaballeROk, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial CentROk de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
ROck.o_MCONROck.o_MCCNROck.o_MCMN
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) ROck(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) ROck(o_MCCN1)
Reports a matrix with the use of class i in each node (server) j in a MultiClass Closed Network
## S3 method for class 'o_MCCN' ROck(x, ...)## S3 method for class 'o_MCCN' ROck(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Reports a matrix with the use of class i in each node (server) j in a MultiClass Closed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) ROck(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) ROck(o_MCCN1)
Reports a matrix with the use of class i in each node (server) j in a MultiClass Mixed Network
## S3 method for class 'o_MCMN' ROck(x, ...)## S3 method for class 'o_MCMN' ROck(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Reports a matrix with the use of class i in each node (server) j in a
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) ROck(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) ROck(o_mcmn1)
Reports a matrix with the use of class i in each node (server) j in a MultiClass Open Network
## S3 method for class 'o_MCON' ROck(x, ...)## S3 method for class 'o_MCON' ROck(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Reports a matrix with the use of class i in each node (server) j in a
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) ROck(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) ROck(o_mcon1)
Reports a vector with each node (server) use of a queueing network
ROk(x, ...)ROk(x, ...)
x |
a object of class o_OJN, o_CJN, o_MCON, o_MCCN, o_MCMN |
... |
aditional arguments |
Reports a vector with each node (server) use of a queueing network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos CaballeROk, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial CentROk de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
ROk.o_OJNROk.o_CJNROk.o_MCONROk.o_MCCNROk.o_MCMN
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) ROk(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) ROk(o_MCCN1)
Reports a vector with each node (server) use of a Closed Jackson Network
## S3 method for class 'o_CJN' ROk(x, ...)## S3 method for class 'o_CJN' ROk(x, ...)
x |
a object of class o_CJN |
... |
aditional arguments |
Reports a vector with each node (server) use of a Closed Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) ROk(m_cjn1)## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) ROk(m_cjn1)
Reports a vector with each node (server) use of a MultiClass Closed Network
## S3 method for class 'o_MCCN' ROk(x, ...)## S3 method for class 'o_MCCN' ROk(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Reports a vector with each node (server) use of a MultiClass Closed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) ROk(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) ROk(o_MCCN1)
Reports a vector with each node (server) use of a MultiClass Mixed Network
## S3 method for class 'o_MCMN' ROk(x, ...)## S3 method for class 'o_MCMN' ROk(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Reports a vector with each node (server) use of a MultiClass Mixed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) ROk(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) ROk(o_mcmn1)
Reports a vector with each node (server) use of a MultiClass Open Network
## S3 method for class 'o_MCON' ROk(x, ...)## S3 method for class 'o_MCON' ROk(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Reports a vector with each node (server) use of a MultiClass Open Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) ROk(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) ROk(o_mcon1)
Reports a vector with each node (server) use of an Open Jackson Network
## S3 method for class 'o_OJN' ROk(x, ...)## S3 method for class 'o_OJN' ROk(x, ...)
x |
a object of class o_OJN |
... |
aditional arguments |
Reports a vector with each node (server) use of an Open Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) # Deinition of the new input i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the models o_ojn <- QueueingModel(i_ojn) ROk(o_ojn)## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) # Deinition of the new input i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the models o_ojn <- QueueingModel(i_ojn) ROk(o_ojn)
Returns the saturation point of a queueing model
SP(x, ...)SP(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Returns the saturation point of a queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=4, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the saturation point SP(o_mm1kk)## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=4, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the saturation point SP(o_mm1kk)
Returns the saturation point, or the maximum number of customers that the M/M/1/K/K queueing model can support with no interference or syncronization between themselves
## S3 method for class 'o_MM1KK' SP(x, ...)## S3 method for class 'o_MM1KK' SP(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
The value returned is the optimal number of customers of a M/M/1/K/K queueing model. It coincides with the inverse of the serialization parameter of Amdahl's Law. That is, the value which converges the speedup func(k) = k/(1 + ser * (k-1)). It makes sense, because the saturation point is the maximun value in which no syncronization happens.
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=4, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the saturation point SP(o_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=4, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the saturation point SP(o_mm1kk)
Summary of the results of a generic Birth and Death process model.
## S3 method for class 'o_BnD' summary(object, ...)## S3 method for class 'o_BnD' summary(object, ...)
object |
a object of class o_BnD |
... |
aditional arguments |
Summaries a generic Birth and Death process model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Build the model o_BnD <- QueueingModel(i_BnD) ## Report the results summary(o_BnD)## Generating a generic Birth and Death model with the same lambda and mu vectors as M/M/1 model ## create input parameters lambda <- rep(1/4, 200) mu <- rep(1/3, 200) i_BnD <- NewInput.BnD(lambda=lambda, mu=mu) ## Build the model o_BnD <- QueueingModel(i_BnD) ## Report the results summary(o_BnD)
Summary of the results of a Closed Jackson Network
## S3 method for class 'o_CJN' summary(object, ...)## S3 method for class 'o_CJN' summary(object, ...)
object |
a object of class o_CJN |
... |
aditional arguments |
Summaries a Closed Jackson Network model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) summary(m_cjn1)## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) summary(m_cjn1)
Summary of the results of a MultiClass Closed Network
## S3 method for class 'o_MCCN' summary(object, ...)## S3 method for class 'o_MCCN' summary(object, ...)
object |
a object of class o_MCCN |
... |
aditional arguments |
Summaries a queueing network model
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) summary(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) summary(o_MCCN1)
Summary of the results of a MultiClass Mixed Network
## S3 method for class 'o_MCMN' summary(object, ...)## S3 method for class 'o_MCMN' summary(object, ...)
object |
a object of class o_MCMN |
... |
aditional arguments |
Summaries a MultiClass Mixed Network model
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) summary(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) summary(o_mcmn1)
Summary of the results of a MultiClass Open Network
## S3 method for class 'o_MCON' summary(object, ...)## S3 method for class 'o_MCON' summary(object, ...)
object |
a object of class o_MCON |
... |
aditional arguments |
Summaries a MultiClass Open Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) summary(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) summary(o_mcon1)
Summary of the results of a M/M/1 queueing model.
## S3 method for class 'o_MM1' summary(object, ...)## S3 method for class 'o_MM1' summary(object, ...)
object |
a object of class o_MM1 |
... |
aditional arguments |
Summaries a M/M/1 queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Report the results summary(o_mm1)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Report the results summary(o_mm1)
Summary of the results of a M/M/1/K queueing model.
## S3 method for class 'o_MM1K' summary(object, ...)## S3 method for class 'o_MM1K' summary(object, ...)
object |
a object of class o_MM1K |
... |
aditional arguments |
Summaries a M/M/1/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Report the results summary(o_mm1k)## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Report the results summary(o_mm1k)
Summary of the results of a M/M/1/K/K queueing model.
## S3 method for class 'o_MM1KK' summary(object, ...)## S3 method for class 'o_MM1KK' summary(object, ...)
object |
a object of class o_MM1KK |
... |
aditional arguments |
Summaries a M/M/1/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Report the results summary(o_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Report the results summary(o_mm1kk)
Summary of the results of a M/M/c queueing model.
## S3 method for class 'o_MMC' summary(object, ...)## S3 method for class 'o_MMC' summary(object, ...)
object |
a object of class o_MMC |
... |
aditional arguments |
Summaries a M/M/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Report the results summary(o_mmc)## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Report the results summary(o_mmc)
Summary of the results of a M/M/c/c queueing model.
## S3 method for class 'o_MMCC' summary(object, ...)## S3 method for class 'o_MMCC' summary(object, ...)
object |
a object of class o_MMCC |
... |
aditional arguments |
Summaries a M/M/c/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Report the results summary(o_mmcc)## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Report the results summary(o_mmcc)
Summary of the results of a M/M/c/K queueing model.
## S3 method for class 'o_MMCK' summary(object, ...)## S3 method for class 'o_MMCK' summary(object, ...)
object |
a object of class o_MMCK |
... |
aditional arguments |
Summaries a M/M/c/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Report the results summary(o_mmck)## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Report the results summary(o_mmck)
Summary of the results of a M/M/c/K/K queueing model.
## S3 method for class 'o_MMCKK' summary(object, ...)## S3 method for class 'o_MMCKK' summary(object, ...)
object |
a object of class o_MMCKK |
... |
aditional arguments |
Summaries a M/M/c/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Report the results summary(o_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Report the results summary(o_mmckk)
Summary of the results of a M/M/c/K/m queueing model.
## S3 method for class 'o_MMCKM' summary(object, ...)## S3 method for class 'o_MMCKM' summary(object, ...)
object |
a object of class o_MMCKM |
... |
aditional arguments |
Summaries a M/M/c/K/m queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Report the results summary(o_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Report the results summary(o_mmckm)
Summary of the results of a M/M/Infinite queueing model.
## S3 method for class 'o_MMInf' summary(object, ...)## S3 method for class 'o_MMInf' summary(object, ...)
object |
a object of class o_MMInf |
... |
aditional arguments |
Summaries a M/M/Infinite queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Report the results summary(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Report the results summary(o_mminf)
Summary of the results of a M/M/Infinite/K/K queueing model.
## S3 method for class 'o_MMInfKK' summary(object, ...)## S3 method for class 'o_MMInfKK' summary(object, ...)
object |
a object of class o_MMInfKK |
... |
aditional arguments |
Summaries a M/M/Infinite/K/K queueing model
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Report the results summary(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Report the results summary(o_MMInfKK)
Summary of the results of an Open Jackson Network
## S3 method for class 'o_OJN' summary(object, ...)## S3 method for class 'o_OJN' summary(object, ...)
object |
a object of class o_OJN |
... |
aditional arguments |
Summaries an Open Jackson Network model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) o_ojn <- QueueingModel(i_ojn) summary(o_ojn)## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) o_ojn <- QueueingModel(i_ojn) summary(o_ojn)
Returns the throughput of a queueing model (or network)
Throughput(x, ...)Throughput(x, ...)
x |
a object of class o_MM1, o_MMC, o_MM1K, o_MMCK, o_MM1KK, o_MMCKK, o_MMCC, o_MMCKM, o_MMInfKK, o_MMInf, o_OJN, o_CJN, o_MCON, o_MCCN, o_MCMN |
... |
aditional arguments |
Returns the throughput of a queueing model (or network)
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
Throughput.o_MM1Throughput.o_MMCThroughput.o_MM1KThroughput.o_MMCKThroughput.o_MM1KKThroughput.o_MMCKKThroughput.o_MMCCThroughput.o_MMCKMThroughput.o_MMInfKKThroughput.o_MMInfThroughput.o_OJNThroughput.o_CJNThroughput.o_MCONThroughput.o_MCCNThroughput.o_MCMN
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Throughput Throughput(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Throughput Throughput(o_mm1)
Reports the network throughput of a Closed Jackson Network
## S3 method for class 'o_CJN' Throughput(x, ...)## S3 method for class 'o_CJN' Throughput(x, ...)
x |
a object of class o_CJN |
... |
aditional arguments |
Reports the network throughput of a Closed Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
NewInput.OJN, CheckInput.i_CJN, QueueingModel.i_CJN
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Throughput(m_cjn1)## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Throughput(m_cjn1)
Reports the throughput of a MultiClass Closed Network
## S3 method for class 'o_MCCN' Throughput(x, ...)## S3 method for class 'o_MCCN' Throughput(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Reports the throughput of a MultiClass Closed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
NewInput.MCCN, CheckInput.i_MCCN, QueueingModel.i_MCCN
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Throughput(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Throughput(o_MCCN1)
Reports the throughput of a MultiClass Mixed Network
## S3 method for class 'o_MCMN' Throughput(x, ...)## S3 method for class 'o_MCMN' Throughput(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Reports the throughput of a MultiClass Mixed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
NewInput.MCMN, CheckInput.i_MCMN, QueueingModel.i_MCMN
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Throughput(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Throughput(o_mcmn1)
Reports the throughput of a MultiClass Open Network
## S3 method for class 'o_MCON' Throughput(x, ...)## S3 method for class 'o_MCON' Throughput(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Reports the throughput of a MultiClass Open Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
NewInput.MCON, CheckInput.i_MCON, QueueingModel.i_MCON
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Throughput(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Throughput(o_mcon1)
Returns the throughput of a M/M/1 queueing model
## S3 method for class 'o_MM1' Throughput(x, ...)## S3 method for class 'o_MM1' Throughput(x, ...)
x |
a object of class o_MM1 |
... |
aditional arguments |
Returns the throughput of a M/M/1 queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
NewInput.MM1, CheckInput.i_MM1, QueueingModel.i_MM1
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Throughput Throughput(o_mm1)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Throughput Throughput(o_mm1)
Returns the throughput of a M/M/1/K queueing model
## S3 method for class 'o_MM1K' Throughput(x, ...)## S3 method for class 'o_MM1K' Throughput(x, ...)
x |
a object of class o_MM1K |
... |
aditional arguments |
Returns the throughput of a M/M/1/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
NewInput.MM1K, CheckInput.i_MM1K, QueueingModel.i_MM1K
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mmck <- QueueingModel(i_mm1k) ## Throughput Throughput(o_mmck)## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mmck <- QueueingModel(i_mm1k) ## Throughput Throughput(o_mmck)
Returns the throughput of a M/M/1/K/K queueing model
## S3 method for class 'o_MM1KK' Throughput(x, ...)## S3 method for class 'o_MM1KK' Throughput(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Returns the throughput of a M/M/1/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
NewInput.MM1KK, CheckInput.i_MM1KK, QueueingModel.i_MM1KK
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_MM1KKk <- QueueingModel(i_mm1kk) ## Throughput Throughput(o_MM1KKk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_MM1KKk <- QueueingModel(i_mm1kk) ## Throughput Throughput(o_MM1KKk)
Returns the throughput of a M/M/c queueing model
## S3 method for class 'o_MMC' Throughput(x, ...)## S3 method for class 'o_MMC' Throughput(x, ...)
x |
a object of class o_MMC |
... |
aditional arguments |
Returns the throughput of a M/M/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
NewInput.MMC, CheckInput.i_MMC, QueueingModel.i_MMC
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Throughput Throughput(o_mmc)## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Throughput Throughput(o_mmc)
Returns the throughput of a M/M/c/c queueing model
## S3 method for class 'o_MMCC' Throughput(x, ...)## S3 method for class 'o_MMCC' Throughput(x, ...)
x |
a object of class o_MMCC |
... |
aditional arguments |
Returns the throughput of a M/M/c/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
NewInput.MMCC, CheckInput.i_MMCC, QueueingModel.i_MMCC
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Throughput Throughput(o_mmcc)## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Throughput Throughput(o_mmcc)
Returns the throughput of a M/M/c/K queueing model
## S3 method for class 'o_MMCK' Throughput(x, ...)## S3 method for class 'o_MMCK' Throughput(x, ...)
x |
a object of class o_MMCK |
... |
aditional arguments |
Returns the throughput of a M/M/c/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
NewInput.MMCK, CheckInput.i_MMCK, QueueingModel.i_MMCK
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Throughput Throughput(o_mmck)## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Throughput Throughput(o_mmck)
Returns the throughput of a M/M/c/K/K queueing model
## S3 method for class 'o_MMCKK' Throughput(x, ...)## S3 method for class 'o_MMCKK' Throughput(x, ...)
x |
a object of class o_MMCKK |
... |
aditional arguments |
Returns the throughput of a M/M/c/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
NewInput.MMCKK, CheckInput.i_MMCKK, QueueingModel.i_MMCKK
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## build the model o_mmckk <- QueueingModel(i_mmckk) ## Throughput Throughput(o_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## build the model o_mmckk <- QueueingModel(i_mmckk) ## Throughput Throughput(o_mmckk)
Returns the throughput of a M/M/c/K/m queueing model
## S3 method for class 'o_MMCKM' Throughput(x, ...)## S3 method for class 'o_MMCKM' Throughput(x, ...)
x |
a object of class o_MMCKM |
... |
aditional arguments |
Returns the throughput of a M/M/c/K/m queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
NewInput.MMCKM, CheckInput.i_MMCKM, QueueingModel.i_MMCKM
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Throughput Throughput(o_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Throughput Throughput(o_mmckm)
Returns the throughput of a M/M/Infinite queueing model
## S3 method for class 'o_MMInf' Throughput(x, ...)## S3 method for class 'o_MMInf' Throughput(x, ...)
x |
a object of class o_MMInf |
... |
aditional arguments |
Returns the throughput of a M/M/Infinite queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
NewInput.MMInf, CheckInput.i_MMInf, QueueingModel.i_MMInf
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Throughput Throughput(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Throughput Throughput(o_mminf)
Returns the throughput of a M/M/Infinite/K/K queueing model
## S3 method for class 'o_MMInfKK' Throughput(x, ...)## S3 method for class 'o_MMInfKK' Throughput(x, ...)
x |
a object of class o_MMInfKK |
... |
aditional arguments |
Returns the throughput of a M/M/Infinite/K/K queueing model
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
NewInput.MMInfKK, CheckInput.i_MMInfKK, QueueingModel.i_MMInfKK
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Throughput Throughput(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Throughput Throughput(o_MMInfKK)
Reports the throughput of an Open Jackson Network
## S3 method for class 'o_OJN' Throughput(x, ...)## S3 method for class 'o_OJN' Throughput(x, ...)
x |
a object of class o_OJN |
... |
aditional arguments |
Reports the throughput of an Open Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
NewInput.OJN, CheckInput.i_OJN, QueueingModel.i_OJN
## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) # Deinition of the new input i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the models o_ojn <- QueueingModel(i_ojn) Throughput(o_ojn)## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) # Deinition of the new input i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the models o_ojn <- QueueingModel(i_ojn) Throughput(o_ojn)
Reports a vector with each class throughput in a multiclass queueing network
Throughputc(x, ...)Throughputc(x, ...)
x |
a object of class o_MCON, o_MCCN, o_MCMN |
... |
aditional arguments |
Reports a vector with each class throughput in a multiclass queueing network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
Throughputc.o_MCONThroughputc.o_MCCNThroughputc.o_MCCN
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Throughputc(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Throughputc(o_mcon1)
Reports a vector with each class throughput in a MultiClass Closed Network
## S3 method for class 'o_MCCN' Throughputc(x, ...)## S3 method for class 'o_MCCN' Throughputc(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Reports a vector with each class throughput in a MultiClass Closed Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
NewInput.MCCN, CheckInput.i_MCCN, QueueingModel.i_MCCN
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Throughputc(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Throughputc(o_MCCN1)
Reports a vector with each class throughput in a MultiClass Mixed Network
## S3 method for class 'o_MCMN' Throughputc(x, ...)## S3 method for class 'o_MCMN' Throughputc(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Reports a vector with each class throughput in a MultiClass Mixed Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
NewInput.MCMN, CheckInput.i_MCMN, QueueingModel.i_MCMN
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Throughputc(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Throughputc(o_mcmn1)
Reports a vector with each class throughput in a MultiClass Open Network
## S3 method for class 'o_MCON' Throughputc(x, ...)## S3 method for class 'o_MCON' Throughputc(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Reports a vector with each class throughput in a MultiClass Open Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
NewInput.MCON, CheckInput.i_MCON, QueueingModel.i_MCON
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Throughputc(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Throughputc(o_mcon1)
Reports a matrix with the throughput of class i in each node (server) j in a MultiClass Network
Throughputck(x, ...)Throughputck(x, ...)
x |
a object of class o_MCON, o_MCCN |
... |
aditional arguments |
Reports a matrix with the throughput of class i in each node (server) j in a MultiClass Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
Throughputck.o_MCONThroughputck.o_MCCNThroughputck.o_MCMN
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Throughputck(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Throughputck(o_mcon1)
Reports a matrix with the throughput of class i in each node (server) j in a MultiClass Closed Network
## S3 method for class 'o_MCCN' Throughputck(x, ...)## S3 method for class 'o_MCCN' Throughputck(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Reports a matrix with the throughput of class i in each node (server) j in a MultiClass Closed Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
NewInput.MCCN, CheckInput.i_MCCN, QueueingModel.i_MCCN
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Throughputck(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Throughputck(o_MCCN1)
Reports a matrix with the throughput of class i in each node (server) j in a MultiClass Mixed Network
## S3 method for class 'o_MCMN' Throughputck(x, ...)## S3 method for class 'o_MCMN' Throughputck(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Reports a matrix with the throughput of class i in each node (server) j in a MultiClass Mixed Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
NewInput.MCMN, CheckInput.i_MCMN, QueueingModel.i_MCMN
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Throughputck(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Throughputck(o_mcmn1)
Reports a matrix with the throughput of class i in each node (server) j in a MultiClass Open Network
## S3 method for class 'o_MCON' Throughputck(x, ...)## S3 method for class 'o_MCON' Throughputck(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Reports a matrix with the throughput of class i in each node (server) j in a MultiClass Open Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
NewInput.MCON, CheckInput.i_MCON, QueueingModel.i_MCON
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Throughputck(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Throughputck(o_mcon1)
Returns a matrix with the Throughput from each class and every population of a Multi Class Closed Network
Throughputcn(x, ...)Throughputcn(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Returns a matrix with the Throughput from each class and every population of a Multi Class Closed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Throughputcn(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Throughputcn(o_MCCN1)
Returns a matrix with the Throughput from each class and every population of a Multi Class Closed Network
## S3 method for class 'o_MCCN' Throughputcn(x, ...)## S3 method for class 'o_MCCN' Throughputcn(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Returns a matrix with the Throughput from each class and every population of a Multi Class Closed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
NewInput.MCCN, CheckInput.i_MCCN, QueueingModel.i_MCCN
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Throughputcn(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Throughputcn(o_MCCN1)
Reports a vector with each node (server) throughput of a queueing network
Throughputk(x, ...)Throughputk(x, ...)
x |
a object of class o_OJN, o_CJN, o_MCON, o_MCCN, o_MCMN |
... |
aditional arguments |
Reports a vector with each node (server) throughput of a queueing network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
Throughputk.o_OJNThroughputk.o_CJNThroughputk.o_MCONThroughputk.o_MCCNThroughputk.o_MCMN
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Throughputk(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Throughputk(o_mcon1)
Reports a vector with each node (server) throughput of a Closed Jackson Network
## S3 method for class 'o_CJN' Throughputk(x, ...)## S3 method for class 'o_CJN' Throughputk(x, ...)
x |
a object of class o_CJN |
... |
aditional arguments |
Reports a vector with each node (server) throughput of a Closed Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
NewInput.CJN, CheckInput.i_CJN, QueueingModel.i_CJN
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Throughputk(m_cjn1)## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Throughputk(m_cjn1)
Reports a vector with each node (server) throughput of a MultiClass Closed Network
## S3 method for class 'o_MCCN' Throughputk(x, ...)## S3 method for class 'o_MCCN' Throughputk(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Reports a vector with each node (server) throughput of a MultiClass Closed Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
NewInput.MCCN, CheckInput.i_MCCN, QueueingModel.i_MCCN
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Throughputk(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Throughputk(o_MCCN1)
Reports a vector with each node (server) throughput of a MultiClass Mixed Network
## S3 method for class 'o_MCMN' Throughputk(x, ...)## S3 method for class 'o_MCMN' Throughputk(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Reports a vector with each node (server) throughput of a MultiClass Mixed Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
NewInput.MCMN, CheckInput.i_MCMN, QueueingModel.i_MCMN
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Throughputk(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Throughputk(o_mcmn1)
Reports a vector with each node (server) throughput of a MultiClass Open Network
## S3 method for class 'o_MCON' Throughputk(x, ...)## S3 method for class 'o_MCON' Throughputk(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Reports a vector with each node (server) throughput of a MultiClass Open Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
NewInput.MCON, CheckInput.i_MCON, QueueingModel.i_MCON
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Throughputk(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Throughputk(o_mcon1)
Reports a vector with each node (server) throughput of an Open Jackson Network
## S3 method for class 'o_OJN' Throughputk(x, ...)## S3 method for class 'o_OJN' Throughputk(x, ...)
x |
a object of class o_OJN |
... |
aditional arguments |
Reports a vector with each node (server) throughput of an Open Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
NewInput.OJN, CheckInput.i_OJN, QueueingModel.i_OJN
## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) # Deinition of the new input i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the models o_ojn <- QueueingModel(i_ojn) Throughputk(o_ojn)## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) # Deinition of the new input i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the models o_ojn <- QueueingModel(i_ojn) Throughputk(o_ojn)
Returns a vector with the each Throughput from 1 to the parameter n (population passed as input) of a Closed Network
Throughputn(x, ...)Throughputn(x, ...)
x |
a object of class o_CJN |
... |
aditional arguments |
Returns a vector with the each Throughput from 1 to the parameter n (population passed as input) of a Closed Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Throughputn(m_cjn1)## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Throughputn(m_cjn1)
Returns a vector with the each Throughput from 1 to the parameter n (population passed as input) of a Closed Jackson Network
## S3 method for class 'o_CJN' Throughputn(x, ...)## S3 method for class 'o_CJN' Throughputn(x, ...)
x |
a object of class o_CJN |
... |
aditional arguments |
Returns a vector with the each Throughput from 1 to the parameter n (population passed as input) of a Closed Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
NewInput.CJN, CheckInput.i_CJN, QueueingModel.i_CJN
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Throughputn(m_cjn1)## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Throughputn(m_cjn1)
Returns the variance of the number of customers in a queueing model (or network)
VN(x, ...)VN(x, ...)
x |
a object of class o_MM1, o_MMC, o_MM1K, o_MMCK, o_MM1KK, o_MMCKK, o_MMCC, o_MMCKM, o_MMInfKK, o_MMInf |
... |
aditional arguments |
Returns the variance of the number of customers in a queueing model (or network)
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
VN.o_MM1VN.o_MMCVN.o_MMCCVN.o_MMInfVN.o_MMInfKKVN.o_MM1KVN.o_MMCKVN.o_MM1KKVN.o_MMCKKVN.o_MMCKM
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance VN(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance VN(o_mm1)
Returns the variance of the number of customers in the M/M/1 queueing model
## S3 method for class 'o_MM1' VN(x, ...)## S3 method for class 'o_MM1' VN(x, ...)
x |
a object of class o_MM1 |
... |
aditional arguments |
Returns the variance of the number of customers in the M/M/1 queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance VN(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance VN(o_mm1)
Returns the variance of the number of customers in the M/M/1/K queueing model
## S3 method for class 'o_MM1K' VN(x, ...)## S3 method for class 'o_MM1K' VN(x, ...)
x |
a object of class o_MM1K |
... |
aditional arguments |
Returns the variance of the number of customers in the M/M/1/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the variance VN(o_mm1k)## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the variance VN(o_mm1k)
Returns the variance of the number of customers in the M/M/1/K/K queueing model
## S3 method for class 'o_MM1KK' VN(x, ...)## S3 method for class 'o_MM1KK' VN(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Returns the variance of the number of customers in the M/M/1/K/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the variance VN(o_mm1kk)## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the variance VN(o_mm1kk)
Returns the variance of the number of customers in the M/M/c queueing model
## S3 method for class 'o_MMC' VN(x, ...)## S3 method for class 'o_MMC' VN(x, ...)
x |
a object of class o_MMC |
... |
aditional arguments |
Returns the variance of the number of customers in the M/M/c queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the variance VN(o_mmc)## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the variance VN(o_mmc)
Returns the variance of the number of customers in the M/M/c/c queueing model
## S3 method for class 'o_MMCC' VN(x, ...)## S3 method for class 'o_MMCC' VN(x, ...)
x |
a object of class o_MMCC |
... |
aditional arguments |
Returns the variance of the number of customers in the M/M/c/c queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the variance VN(o_mmcc)## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the variance VN(o_mmcc)
Returns the variance of the number of customers in the M/M/c/K queueing model
## S3 method for class 'o_MMCK' VN(x, ...)## S3 method for class 'o_MMCK' VN(x, ...)
x |
a object of class o_MMCK |
... |
aditional arguments |
Returns the variance of the number of customers in the M/M/c/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the variance VN(o_mmck)## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the variance VN(o_mmck)
Returns the variance of the number of customers in the M/M/c/K/K queueing model
## S3 method for class 'o_MMCKK' VN(x, ...)## S3 method for class 'o_MMCKK' VN(x, ...)
x |
a object of class o_MMCKK |
... |
aditional arguments |
Returns the variance of the number of customers in the M/M/c/K/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the variance VN(o_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the variance VN(o_mmckk)
Returns the variance of the number of customers in the M/M/c/K/m queueing model
## S3 method for class 'o_MMCKM' VN(x, ...)## S3 method for class 'o_MMCKM' VN(x, ...)
x |
a object of class o_MMCKM |
... |
aditional arguments |
Returns the variance of the number of customers in the M/M/c/K/m queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the variance VN(o_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the variance VN(o_mmckm)
Returns the variance of the number of customers in the M/M/Infinite queueing model
## S3 method for class 'o_MMInf' VN(x, ...)## S3 method for class 'o_MMInf' VN(x, ...)
x |
a object of class o_MMInf |
... |
aditional arguments |
Returns the variance of the number of customers in the M/M/Infinite queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the variance VN(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the variance VN(o_mminf)
Returns the variance of the number of customers in the M/M/Infinite/K/K queueing model
## S3 method for class 'o_MMInfKK' VN(x, ...)## S3 method for class 'o_MMInfKK' VN(x, ...)
x |
a object of class o_MMInfKK |
... |
aditional arguments |
Returns the variance of the number of customers in the M/M/Infinite/K/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the variance VN(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the variance VN(o_MMInfKK)
Returns the variance of the number of customers in the queue in a queueing model
VNq(x, ...)VNq(x, ...)
x |
a object of class o_MM1, o_MMC, o_MM1K, o_MMCK, o_MM1KK, o_MMCKK, o_MMCC, o_MMCKM, o_MMInfKK, o_MMInf |
... |
aditional arguments |
Returns the variance of the number of customers in the queue in a queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
VNq.o_MM1VNq.o_MM1VNq.o_MMCCVNq.o_MMInfVNq.o_MMInfKKVNq.o_MM1KVNq.o_MMCKVNq.o_MM1KKVNq.o_MMCKKVNq.o_MMCKM
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance VNq(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance VNq(o_mm1)
Returns the variance of the number of customers in the queue in the M/M/1 queueing model
## S3 method for class 'o_MM1' VNq(x, ...)## S3 method for class 'o_MM1' VNq(x, ...)
x |
a object of class o_MM1 |
... |
aditional arguments |
Returns the variance of the number of customers in the queue in the M/M/1 queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance VNq(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance VNq(o_mm1)
Returns the variance of the number of customers in the queue in the M/M/1/K queueing model
## S3 method for class 'o_MM1K' VNq(x, ...)## S3 method for class 'o_MM1K' VNq(x, ...)
x |
a object of class o_MM1K |
... |
aditional arguments |
Returns the variance of the number of customers in the queue in the M/M/1/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the variance VNq(o_mm1k)## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the variance VNq(o_mm1k)
Returns the variance of the number of customers in the queue in the M/M/1/K/K queueing model
## S3 method for class 'o_MM1KK' VNq(x, ...)## S3 method for class 'o_MM1KK' VNq(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Returns the variance of the number of customers in the queue in the M/M/1/K/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the variance VNq(o_mm1kk)## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the variance VNq(o_mm1kk)
Returns the variance of the number of customers in the queue in the M/M/c queueing model
## S3 method for class 'o_MMC' VNq(x, ...)## S3 method for class 'o_MMC' VNq(x, ...)
x |
a object of class o_MMC |
... |
aditional arguments |
Returns the variance of the number of customers in the queue in the M/M/c queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the variance VNq(o_mmc)## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the variance VNq(o_mmc)
Returns the variance of the number of customers in the queue in the M/M/c/c queueing model
## S3 method for class 'o_MMCC' VNq(x, ...)## S3 method for class 'o_MMCC' VNq(x, ...)
x |
a object of class o_MMCC |
... |
aditional arguments |
Returns the variance of the number of customers in the queue in the M/M/c/c queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the variance VNq(o_mmcc)## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the variance VNq(o_mmcc)
Returns the variance of the number of customers in the queue in the M/M/c/K queueing model
## S3 method for class 'o_MMCK' VNq(x, ...)## S3 method for class 'o_MMCK' VNq(x, ...)
x |
a object of class o_MMCK |
... |
aditional arguments |
Returns the variance of the number of customers in the queue in the M/M/c/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the variance VNq(o_mmck)## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the variance VNq(o_mmck)
Returns the variance of the number of customers in the queue in the M/M/c/K/K queueing model
## S3 method for class 'o_MMCKK' VNq(x, ...)## S3 method for class 'o_MMCKK' VNq(x, ...)
x |
a object of class o_MMCKK |
... |
aditional arguments |
Returns the variance of the number of customers in the queue in the M/M/c/K/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the variance VNq(o_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the variance VNq(o_mmckk)
Returns the variance of the number of customers in the queue in the M/M/c/K/m queueing model
## S3 method for class 'o_MMCKM' VNq(x, ...)## S3 method for class 'o_MMCKM' VNq(x, ...)
x |
a object of class o_MMCKM |
... |
aditional arguments |
Returns the variance of the number of customers in the queue in the M/M/c/K/m queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the variance VNq(o_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the variance VNq(o_mmckm)
Returns the variance of the number of customers in the queue in the M/M/Infinite queueing model
## S3 method for class 'o_MMInf' VNq(x, ...)## S3 method for class 'o_MMInf' VNq(x, ...)
x |
a object of class o_MMInf |
... |
aditional arguments |
Returns the variance of the number of customers in the queue in the M/M/Infinite queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the variance VNq(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the variance VNq(o_mminf)
Returns the variance of the number of customers in the queue in the M/M/Infinite/K/K queueing model
## S3 method for class 'o_MMInfKK' VNq(x, ...)## S3 method for class 'o_MMInfKK' VNq(x, ...)
x |
a object of class o_MMInfKK |
... |
aditional arguments |
Returns the variance of the number of customers in the queue in the M/M/Infinite/K/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the VNq VNq(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the VNq VNq(o_MMInfKK)
Returns the variance of the time spend in a queueing model (or network)
VT(x, ...)VT(x, ...)
x |
a object of class o_MM1, o_MMC, o_MM1K, o_MMCK, o_MM1KK, o_MMCKK, o_MMCC, o_MMCKM, o_MMInfKK, o_MMInf |
... |
aditional arguments |
Returns the variance of the time spend in a queueing model (or network)
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
VT.o_MM1VT.o_MMCVT.o_MMCCVT.o_MMInfVT.o_MMInfKKVT.o_MM1KVT.o_MM1KK
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance of the time spend in the system VT(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance of the time spend in the system VT(o_mm1)
Returns the variance of the time spend in the M/M/1 queueing model
## S3 method for class 'o_MM1' VT(x, ...)## S3 method for class 'o_MM1' VT(x, ...)
x |
a object of class o_MM1 |
... |
aditional arguments |
Returns the variance of the time spend in the M/M/1 queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance of the time spend in the system VT(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance of the time spend in the system VT(o_mm1)
Returns the variance of the time spend in the M/M/1/K queueing model
## S3 method for class 'o_MM1K' VT(x, ...)## S3 method for class 'o_MM1K' VT(x, ...)
x |
a object of class o_MM1K |
... |
aditional arguments |
Returns the variance of the time spend in the M/M/1/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the variance VT(o_mm1k)## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the variance VT(o_mm1k)
Returns the variance of the time spend in the M/M/1/K/K queueing model
## S3 method for class 'o_MM1KK' VT(x, ...)## S3 method for class 'o_MM1KK' VT(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Returns the variance of the time spend in the M/M/1/K/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the variance VT(o_mm1kk)## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the variance VT(o_mm1kk)
Returns the variance of the time spend in the M/M/c queueing model
## S3 method for class 'o_MMC' VT(x, ...)## S3 method for class 'o_MMC' VT(x, ...)
x |
a object of class o_MMC |
... |
aditional arguments |
Returns the variance of the time spend in the M/M/c queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the variance of the time spend in the system VT(o_mmc)## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the variance of the time spend in the system VT(o_mmc)
Returns the variance of the time spend in the M/M/c/c queueing model
## S3 method for class 'o_MMCC' VT(x, ...)## S3 method for class 'o_MMCC' VT(x, ...)
x |
a object of class o_MMCC |
... |
aditional arguments |
Returns the variance of the time spend in the M/M/c/c queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the variance VT(o_mmcc)## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the variance VT(o_mmcc)
Returns the variance of the time spend in the M/M/Infinite queueing model
## S3 method for class 'o_MMInf' VT(x, ...)## S3 method for class 'o_MMInf' VT(x, ...)
x |
a object of class o_MMInf |
... |
aditional arguments |
Returns the the variance of the time spend in the M/M/Infinite queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the variance VT(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the variance VT(o_mminf)
Returns the variance of the time spend in the M/M/Infinite/K/K queueing model
## S3 method for class 'o_MMInfKK' VT(x, ...)## S3 method for class 'o_MMInfKK' VT(x, ...)
x |
a object of class o_MMInfKK |
... |
aditional arguments |
Returns the variance of the time spend in the M/M/Infinite/K/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the variance VT(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the variance VT(o_MMInfKK)
Returns the variance of the time spend in queue in a queueing model
VTq(x, ...)VTq(x, ...)
x |
a object of class o_MM1, o_MMC, o_MM1K, o_MMCK, o_MM1KK, o_MMCKK, o_MMCC, o_MMCKM, o_MMInfKK, o_MMInf |
... |
aditional arguments |
Returns the variance of the time spend in queue in a queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
VTq.o_MM1VTq.o_MMCVTq.o_MMCCVTq.o_MMInfVTq.o_MMInfKKVTq.o_MM1KVTq.o_MMCKVTq.o_MM1KKVTq.o_MMCKK
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance of the time spend in queue VTq(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance of the time spend in queue VTq(o_mm1)
Returns the variance of the time spend in queue in the M/M/1 queueing model
## S3 method for class 'o_MM1' VTq(x, ...)## S3 method for class 'o_MM1' VTq(x, ...)
x |
a object of class o_MM1 |
... |
aditional arguments |
Returns the variance of the time spend in queue in the M/M/1 queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance of the time spend in queue VTq(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the variance of the time spend in queue VTq(o_mm1)
Returns the variance of the time spend in queue in the M/M/1/K queueing model
## S3 method for class 'o_MM1K' VTq(x, ...)## S3 method for class 'o_MM1K' VTq(x, ...)
x |
a object of class o_MM1K |
... |
aditional arguments |
Returns the variance of the time spend in queue in the M/M/1/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the variance VTq(o_mm1k)## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the variance VTq(o_mm1k)
Returns the variance of the time spend in queue in the M/M/1/K/K queueing model
## S3 method for class 'o_MM1KK' VTq(x, ...)## S3 method for class 'o_MM1KK' VTq(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Returns the variance of the time spend in queue in the M/M/1/K/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the VTq VTq(o_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the VTq VTq(o_mm1kk)
Returns the variance of the time spend in queue in the M/M/c queueing model
## S3 method for class 'o_MMC' VTq(x, ...)## S3 method for class 'o_MMC' VTq(x, ...)
x |
a object of class o_MMC |
... |
aditional arguments |
Returns the variance of the time spend in queue in the M/M/c queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the variance of the time spend in queue VTq(o_mmc)## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the variance of the time spend in queue VTq(o_mmc)
Returns the variance of the time spend in queue in the M/M/c/c queueing model
## S3 method for class 'o_MMCC' VTq(x, ...)## S3 method for class 'o_MMCC' VTq(x, ...)
x |
a object of class o_MMCC |
... |
aditional arguments |
Returns the variance of the time spend in queue in the M/M/c/c queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the variance VTq(o_mmcc)## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the variance VTq(o_mmcc)
Returns the variance of the time spend in queue in the M/M/c/K queueing model
## S3 method for class 'o_MMCK' VTq(x, ...)## S3 method for class 'o_MMCK' VTq(x, ...)
x |
a object of class o_MMCK |
... |
aditional arguments |
Returns the variance of the time spend in queue in the M/M/c/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the variance VTq(o_mmck)## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the variance VTq(o_mmck)
Returns the variance of the time spend in queue in the M/M/c/K/K queueing model
## S3 method for class 'o_MMCKK' VTq(x, ...)## S3 method for class 'o_MMCKK' VTq(x, ...)
x |
a object of class o_MMCKK |
... |
aditional arguments |
Returns the variance of the time spend in queue in the M/M/c/K/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the variance VTq(o_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the variance VTq(o_mmckk)
Returns the variance of the time spend in queue in the M/M/Infinite queueing model
## S3 method for class 'o_MMInf' VTq(x, ...)## S3 method for class 'o_MMInf' VTq(x, ...)
x |
a object of class o_MMInf |
... |
aditional arguments |
Returns the variance of the time spend in queue in the M/M/Infinite queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the variance VTq(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the variance VTq(o_mminf)
Returns the variance of the time spend in queue in the M/M/Infinite/K/K queueing model
## S3 method for class 'o_MMInfKK' VTq(x, ...)## S3 method for class 'o_MMInfKK' VTq(x, ...)
x |
a object of class o_MMInfKK |
... |
aditional arguments |
Returns the variance of the time spend in queue in the M/M/Infinite/K/K queueing model
[Sztrik2012] Dr. Janos Sztrik (2012).
Basic Queueing Theory.
University of Debrecen, Faculty of Informatics.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the variance VTq(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the variance VTq(o_MMInfKK)
Returns the mean time spend in a queueing model (or network)
W(x, ...)W(x, ...)
x |
a object of class o_MM1, o_MMC, o_MM1K, o_MMCK, o_MM1KK, o_MMCKK, o_MMCC, o_MMCKM, o_MMInfKK, o_MMInf, o_OJN, o_MCON, o_MCCN, o_MCMN |
... |
aditional arguments |
Returns the mean time spend in a queueing model (or network)
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
W.o_MM1W.o_MMCW.o_MM1KW.o_MMCKW.o_MM1KKW.o_MMCKKW.o_MMCCW.o_MMCKMW.o_MMInfKKW.o_MMInfW.o_OJNW.o_MCONW.o_MCCNW.o_MCMN
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the W W(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the W W(o_mm1)
Returns the mean time spend in a Closed Jackson Network
## S3 method for class 'o_CJN' W(x, ...)## S3 method for class 'o_CJN' W(x, ...)
x |
a object of class o_CJN |
... |
aditional arguments |
Returns the mean time spend in a Closed Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) W(m_cjn1)## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) W(m_cjn1)
Returns the mean time spend in a MultiClass Closed Network
## S3 method for class 'o_MCCN' W(x, ...)## S3 method for class 'o_MCCN' W(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Returns the mean time spend in a MultiClass Closed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) W(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) W(o_MCCN1)
Returns the mean time spend in a MultiClass Mixed Network
## S3 method for class 'o_MCMN' W(x, ...)## S3 method for class 'o_MCMN' W(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Returns the mean time spend in a MultiClass Mixed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) W(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) W(o_mcmn1)
Returns the mean time spend in a MultiClass Open Network
## S3 method for class 'o_MCON' W(x, ...)## S3 method for class 'o_MCON' W(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Returns the mean time spend in a MultiClass Open Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) W(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) W(o_mcon1)
Returns the mean time spend in the M/M/1 queueing model
## S3 method for class 'o_MM1' W(x, ...)## S3 method for class 'o_MM1' W(x, ...)
x |
a object of class o_MM1 |
... |
aditional arguments |
Returns the mean time spend in the M/M/1 queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the W W(o_mm1)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the W W(o_mm1)
Returns the mean time spend in the M/M/1/K queueing model
## S3 method for class 'o_MM1K' W(x, ...)## S3 method for class 'o_MM1K' W(x, ...)
x |
a object of class o_MM1K |
... |
aditional arguments |
Returns the mean time spend in the M/M/1/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the W W(o_mm1k)## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the W W(o_mm1k)
Returns the mean time spend in the M/M/1/K/K queueing model
## S3 method for class 'o_MM1KK' W(x, ...)## S3 method for class 'o_MM1KK' W(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Returns the mean time spend in the M/M/1/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the W W(o_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the W W(o_mm1kk)
Returns the mean time spend in the M/M/c queueing model
## S3 method for class 'o_MMC' W(x, ...)## S3 method for class 'o_MMC' W(x, ...)
x |
a object of class o_MMC |
... |
aditional arguments |
Returns the mean time spend in the M/M/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the W W(o_mmc)## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the W W(o_mmc)
Returns the mean time spend in the M/M/c/c queueing model
## S3 method for class 'o_MMCC' W(x, ...)## S3 method for class 'o_MMCC' W(x, ...)
x |
a object of class o_MMCC |
... |
aditional arguments |
Returns the mean time spend in the M/M/c/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the W W(o_mmcc)## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the W W(o_mmcc)
Returns the mean time spend in the M/M/c/K queueing model
## S3 method for class 'o_MMCK' W(x, ...)## S3 method for class 'o_MMCK' W(x, ...)
x |
a object of class o_MMCK |
... |
aditional arguments |
Returns the mean time spend in the M/M/c/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the W W(o_mmck)## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the W W(o_mmck)
Returns the mean time spend in the M/M/c/K/K queueing model
## S3 method for class 'o_MMCKK' W(x, ...)## S3 method for class 'o_MMCKK' W(x, ...)
x |
a object of class o_MMCKK |
... |
aditional arguments |
Returns the mean time spend in the M/M/c/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the W W(o_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the W W(o_mmckk)
Returns the mean time spend in the M/M/c/K/m queueing model
## S3 method for class 'o_MMCKM' W(x, ...)## S3 method for class 'o_MMCKM' W(x, ...)
x |
a object of class o_MMCKM |
... |
aditional arguments |
Returns the mean time spend in the M/M/c/K/m queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the W W(o_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the W W(o_mmckm)
Returns the mean time spend in the M/M/Infinite queueing model
## S3 method for class 'o_MMInf' W(x, ...)## S3 method for class 'o_MMInf' W(x, ...)
x |
a object of class o_MMInf |
... |
aditional arguments |
Returns the mean time spend in the M/M/Infinite queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the W W(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the W W(o_mminf)
Returns the mean time spend in the M/M/Infinite/K/K queueing model
## S3 method for class 'o_MMInfKK' W(x, ...)## S3 method for class 'o_MMInfKK' W(x, ...)
x |
a object of class o_MMInfKK |
... |
aditional arguments |
Returns the mean time spend in the M/M/Infinite/K/K queueing model
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the W W(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the W W(o_MMInfKK)
Returns the mean time spend in an Open Jackson Network
## S3 method for class 'o_OJN' W(x, ...)## S3 method for class 'o_OJN' W(x, ...)
x |
a object of class o_OJN |
... |
aditional arguments |
Returns the mean time spend in an Open Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) # Deinition of the new input i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the models o_ojn <- QueueingModel(i_ojn) W(o_ojn)## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) # Deinition of the new input i_ojn <- NewInput.OJN(prob, n1, n2, n3, n4) # Build the models o_ojn <- QueueingModel(i_ojn) W(o_ojn)
Returns the vector with each class mean time spend on a multiclass queueing network
Wc(x, ...)Wc(x, ...)
x |
a object of class o_MCON, o_MCCN, o_MCMN |
... |
aditional arguments |
Returns the vector with each class mean time spend on a multiclass queueing network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Wc(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Wc(o_mcon1)
Returns the vector with each class mean time spend on a MultiClass Closed Network
## S3 method for class 'o_MCCN' Wc(x, ...)## S3 method for class 'o_MCCN' Wc(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Returns the vector with each class mean time spend on a MultiClass Closed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Wc(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Wc(o_MCCN1)
Returns the vector with each class mean time spend on a MultiClass Mixed Network
## S3 method for class 'o_MCMN' Wc(x, ...)## S3 method for class 'o_MCMN' Wc(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Returns the vector with each class mean time spend on a MultiClass Mixed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Wc(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Wc(o_mcmn1)
Returns the vector with each class mean time spend on a MultiClass Open Network
## S3 method for class 'o_MCON' Wc(x, ...)## S3 method for class 'o_MCON' Wc(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Returns the vector with each class mean time spend on a MultiClass Open Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Wc(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Wc(o_mcon1)
Reports a matrix with the mean time of class i in each node (server) j in a MultiClass Queueing Network
Wck(x, ...)Wck(x, ...)
x |
a object of class o_MCON, o_MCCN, o_MCMN |
... |
aditional arguments |
Reports a matrix with the mean time of class i in each node (server) j in a MultiClass Queueing Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
Wck.o_MCONWck.o_MCCNWck.o_MCMN
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Wck(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Wck(o_mcon1)
Reports a matrix with the mean time of class i in each node (server) j in a MultiClass Closed Network
## S3 method for class 'o_MCCN' Wck(x, ...)## S3 method for class 'o_MCCN' Wck(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Reports a matrix with the mean time of class i in each node (server) j in a MultiClass Closed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Wck(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Wck(o_MCCN1)
Reports a matrix with the mean time of class i in each node (server) j in a MultiClass Mixed Network
## S3 method for class 'o_MCMN' Wck(x, ...)## S3 method for class 'o_MCMN' Wck(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Reports a matrix with the mean time of class i in each node (server) j in a MultiClass Mixed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Wck(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Wck(o_mcmn1)
Reports a matrix with the mean time of class i in each node (server) j in a MultiClass Open Network
## S3 method for class 'o_MCON' Wck(x, ...)## S3 method for class 'o_MCON' Wck(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Reports a matrix with the mean time of class i in each node (server) j in a MultiClass Open Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Wck(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Wck(o_mcon1)
Generic S3 method to return the mean time spend in each node (or server) of a network
Wk(x, ...)Wk(x, ...)
x |
a object of class o_OJN, o_CJN, o_MCON, o_MCCN, o_MCMN |
... |
aditional arguments |
Generic S3 method to return the mean time spend in each node (or server) of a network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
Wk.o_OJNWk.o_CJNWk.o_MCONWk.o_MCCNWk.o_MCMN
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Wk(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Wk(o_mcon1)
Returns the vector with the mean time spend in each node (server) of a Closed Jackson Network
## S3 method for class 'o_CJN' Wk(x, ...)## S3 method for class 'o_CJN' Wk(x, ...)
x |
a object of class o_CJN |
... |
aditional arguments |
Returns the vector with the mean time spend in each node (server) of a Closed Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Wk(m_cjn1)## See example 11.13 in reference [Sixto2004] for more details. ## create the nodes n <- 2 n1 <- NewInput.MM1(lambda=0, mu=1/0.2, n=0) n2 <- NewInput.MM1(lambda=0, mu=1/0.4, n=0) # think time = 0 z <- 0 # operational value operational <- FALSE # definition of the transition probabilities prob <- matrix(data=c(0.5, 0.5, 0.5, 0.5), nrow=2, ncol=2, byrow=TRUE) # Define a new input cjn1 <- NewInput.CJN(prob, n, z, operational, 0, 0.001, n1, n2) # Check the inputs and build the model m_cjn1 <- QueueingModel(cjn1) Wk(m_cjn1)
Returns a vector with the mean time spend in each node (server) of a MultiClass Closed Network
## S3 method for class 'o_MCCN' Wk(x, ...)## S3 method for class 'o_MCCN' Wk(x, ...)
x |
a object of class o_MCCN |
... |
aditional arguments |
Returns a vector with the mean time spend in each node (server) of a MultiClass Closed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Wk(o_MCCN1)## See example in pag 142 in reference [Lazowska84] for more details. classes <- 2 vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_MCCN1 <- NewInput.MCCN(classes, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_MCCN1 <- QueueingModel(i_MCCN1) Wk(o_MCCN1)
Returns a matrix with the mean time spend in each node (server) of a MultiClass Mixed Network
## S3 method for class 'o_MCMN' Wk(x, ...)## S3 method for class 'o_MCMN' Wk(x, ...)
x |
a object of class o_MCMN |
... |
aditional arguments |
Returns a matrix with the mean time spend in each node (server) of a MultiClass Mixed Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Wk(o_mcmn1)## See example in pag 147 in reference [Lazowska84] for more details. classes <- 4 vLambda <- c(1, 1/2) vNumber <- c(1, 1) vThink <- c(0, 0) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=1, nrow=4, ncol=2) vService <- matrix(data=c(1/4, 1/2, 1/2, 1, 1/6, 1, 1, 4/3), nrow=4, ncol=2) i_mcmn1 <- NewInput.MCMN(classes, vLambda, vNumber, vThink, nodes, vType, vVisit, vService) # Build the model o_mcmn1 <- QueueingModel(i_mcmn1) Wk(o_mcmn1)
Returns a matrix with the mean time spend in each node (server) of a MultiClass Open Network
## S3 method for class 'o_MCON' Wk(x, ...)## S3 method for class 'o_MCON' Wk(x, ...)
x |
a object of class o_MCON |
... |
aditional arguments |
Returns a matrix with the mean time spend in each node (server) of a MultiClass Open Network
[Lazowska84] Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik (1984).
Quantitative System Performance: Computer System Analysis Using Queueing Network Models.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey
## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Wk(o_mcon1)## See example in pag 138 in reference [Lazowska84] for more details. classes <- 2 vLambda <- c(3/19, 2/19) nodes <- 2 vType <- c("Q", "Q") vVisit <- matrix(data=c(10, 9, 5, 4), nrow=2, ncol=2, byrow=TRUE) vService <- matrix(data=c(1/10, 1/3, 2/5, 1), nrow=2, ncol=2, byrow=TRUE) i_mcon1 <- NewInput.MCON(classes, vLambda, nodes, vType, vVisit, vService) # Build the model o_mcon1 <- QueueingModel(i_mcon1) Wk(o_mcon1)
Returns the vector with the mean time spend in each node (server) of an Open Jackson Network
## S3 method for class 'o_OJN' Wk(x, ...)## S3 method for class 'o_OJN' Wk(x, ...)
x |
a object of class o_OJN |
... |
aditional arguments |
Returns the vector with the mean time spend in each node (server) of an Open Jackson Network
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) ojn1 <- NewInput.OJN(prob, n1, n2, n3, n4) m_ojn1 <- QueueingModel(ojn1) Wk(m_ojn1)## See example 11.11 in reference [Sixto2004] for more details. ## create the nodes n1 <- NewInput.MM1(lambda=8, mu=14, n=0) n2 <- NewInput.MM1(lambda=0, mu=9, n=0) n3 <- NewInput.MM1(lambda=6, mu=17, n=0) n4 <- NewInput.MM1(lambda=0, mu=7, n=0) m <- c(0, 0.2, 0.56, 0.24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) # definition of the transition probabilities prob <- matrix(data=m, nrow=4, ncol=4, byrow=TRUE) ojn1 <- NewInput.OJN(prob, n1, n2, n3, n4) m_ojn1 <- QueueingModel(ojn1) Wk(m_ojn1)
Returns the mean time spend in queue in a queueing model
Wq(x, ...)Wq(x, ...)
x |
a object of class o_MM1, o_MMC, o_MM1K, o_MMCK, o_MM1KK, o_MMCKK, o_MMCC, o_MMCKM, o_MMInfKK, o_MMInf |
... |
aditional arguments |
Returns the mean time spend in queue in a queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
Wq.o_MM1Wq.o_MMCWq.o_MM1KWq.o_MMCKWq.o_MM1KKWq.o_MMCKKWq.o_MMCCWq.o_MMCKMWq.o_MMInfKKWq.o_MMInf
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Wq Wq(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Wq Wq(o_mm1)
Returns the mean time spend in queue in the M/M/1 queueing model
## S3 method for class 'o_MM1' Wq(x, ...)## S3 method for class 'o_MM1' Wq(x, ...)
x |
a object of class o_MM1 |
... |
aditional arguments |
Returns the mean time spend in queue in the M/M/1 queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Wq Wq(o_mm1)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Wq Wq(o_mm1)
Returns the mean time spend in queue in the M/M/1/K queueing model
## S3 method for class 'o_MM1K' Wq(x, ...)## S3 method for class 'o_MM1K' Wq(x, ...)
x |
a object of class o_MM1K |
... |
aditional arguments |
Returns the mean time spend in queue in the M/M/1/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the Wq Wq(o_mm1k)## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the Wq Wq(o_mm1k)
Returns the mean time spend in queue in the M/M/1/K/K queueing model
## S3 method for class 'o_MM1KK' Wq(x, ...)## S3 method for class 'o_MM1KK' Wq(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Returns the mean time spend in queue in the M/M/1/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the Wq Wq(o_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the Wq Wq(o_mm1kk)
Returns the mean time spend in queue in the M/M/c queueing model
## S3 method for class 'o_MMC' Wq(x, ...)## S3 method for class 'o_MMC' Wq(x, ...)
x |
a object of class o_MMC |
... |
aditional arguments |
Returns the mean time spend in queue in the M/M/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the Wq Wq(o_mmc)## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the Wq Wq(o_mmc)
Returns the mean time spend in queue in the M/M/c/c queueing model
## S3 method for class 'o_MMCC' Wq(x, ...)## S3 method for class 'o_MMCC' Wq(x, ...)
x |
a object of class o_MMCC |
... |
aditional arguments |
Returns the mean time spend in queue in the M/M/c/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the Wq Wq(o_mmcc)## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the Wq Wq(o_mmcc)
Returns the mean time spend in queue in the M/M/c/K queueing model
## S3 method for class 'o_MMCK' Wq(x, ...)## S3 method for class 'o_MMCK' Wq(x, ...)
x |
a object of class o_MMCK |
... |
aditional arguments |
Returns the mean time spend in queue in the M/M/c/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the Wq Wq(o_mmck)## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the Wq Wq(o_mmck)
Returns the mean time spend in queue in the M/M/c/K/K queueing model
## S3 method for class 'o_MMCKK' Wq(x, ...)## S3 method for class 'o_MMCKK' Wq(x, ...)
x |
a object of class o_MMCKK |
... |
aditional arguments |
Returns the mean time spend in queue in the M/M/c/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the Wq Wq(o_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the Wq Wq(o_mmckk)
Returns the mean time spend in queue in the M/M/c/K/m queueing model
## S3 method for class 'o_MMCKM' Wq(x, ...)## S3 method for class 'o_MMCKM' Wq(x, ...)
x |
a object of class o_MMCKM |
... |
aditional arguments |
Returns the mean time spend in queue in the M/M/c/K/m queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the Wq Wq(o_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the Wq Wq(o_mmckm)
Returns the mean time spend in queue in the M/M/Infinite queueing model
## S3 method for class 'o_MMInf' Wq(x, ...)## S3 method for class 'o_MMInf' Wq(x, ...)
x |
a object of class o_MMInf |
... |
aditional arguments |
Returns the mean time spend in queue in the M/M/Infinite queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the Wq Wq(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the Wq Wq(o_mminf)
Returns the mean time spend in queue in the M/M/Infinite/K/K queueing model
## S3 method for class 'o_MMInfKK' Wq(x, ...)## S3 method for class 'o_MMInfKK' Wq(x, ...)
x |
a object of class o_MMInfKK |
... |
aditional arguments |
Returns the mean time spend in queue in the M/M/Infinite/K/K queueing model
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the Wq Wq(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the Wq Wq(o_MMInfKK)
Returns the mean time spend in queue when there is queue in a queueing model
Wqq(x, ...)Wqq(x, ...)
x |
a object of class o_MM1, o_MMC, o_MM1K, o_MMCK, o_MM1KK, o_MMCKK, o_MMCC, o_MMCKM, o_MMInfKK, o_MMInf |
... |
aditional arguments |
Returns the mean time spend in queue when there is queue in a queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
Wqq.o_MM1Wqq.o_MMCWqq.o_MM1KWqq.o_MMCKWqq.o_MM1KKWqq.o_MMCKKWqq.o_MMCCWqq.o_MMCKMWqq.o_MMInfKKWqq.o_MMInf
## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Wqq Wqq(o_mm1)## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Wqq Wqq(o_mm1)
Returns the mean time spend in queue when there is queue in the M/M/1 queueing model
## S3 method for class 'o_MM1' Wqq(x, ...)## S3 method for class 'o_MM1' Wqq(x, ...)
x |
a object of class o_MM1 |
... |
aditional arguments |
Returns the mean time spend in queue when there is queue in the M/M/1 queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Wqq Wqq(o_mm1)## See example 10.3 in reference [Sixto2004] for more details. ## create input parameters i_mm1 <- NewInput.MM1(lambda=1/4, mu=1/3, n=0) ## Build the model o_mm1 <- QueueingModel(i_mm1) ## Returns the Wqq Wqq(o_mm1)
Returns the mean time spend in queue when there is queue in the M/M/1/K queueing model
## S3 method for class 'o_MM1K' Wqq(x, ...)## S3 method for class 'o_MM1K' Wqq(x, ...)
x |
a object of class o_MM1K |
... |
aditional arguments |
Returns the mean time spend in queue when there is queue in the M/M/1/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the Wqq Wqq(o_mm1k)## See example 10.7 in reference [Sixto2004] for more details. ## create input parameters i_mm1k <- NewInput.MM1K(lambda=5, mu=5.714, k=15) ## Build the model o_mm1k <- QueueingModel(i_mm1k) ## Returns the Wqq Wqq(o_mm1k)
Returns the mean time spend in queue when there is queue in the M/M/1/K/K queueing model
## S3 method for class 'o_MM1KK' Wqq(x, ...)## S3 method for class 'o_MM1KK' Wqq(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Returns the mean time spend in queue when there is queue in the M/M/1/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the Wqq Wqq(o_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the Wqq Wqq(o_mm1kk)
Returns the mean time spend in queue when there is queue in the M/M/c queueing model
## S3 method for class 'o_MMC' Wqq(x, ...)## S3 method for class 'o_MMC' Wqq(x, ...)
x |
a object of class o_MMC |
... |
aditional arguments |
Returns the mean time spend in queue when there is queue in the M/M/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the Wqq Wqq(o_mmc)## See example 10.9 in reference [Sixto2004] for more details. ## create input parameters i_mmc <- NewInput.MMC(lambda=5, mu=10, c=2, n=0, method=0) ## Build the model o_mmc <- QueueingModel(i_mmc) ## Returns the Wqq Wqq(o_mmc)
Returns the mean time spend in queue when there is queue in the M/M/c/c queueing model
## S3 method for class 'o_MMCC' Wqq(x, ...)## S3 method for class 'o_MMCC' Wqq(x, ...)
x |
a object of class o_MMCC |
... |
aditional arguments |
Returns the mean time spend in queue when there is queue in the M/M/c/c queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the Wqq Wqq(o_mmcc)## See example 10.12 in reference [Sixto2004] for more details. ## create input parameters i_mmcc <- NewInput.MMCC(lambda=3, mu=0.25, c=15) ## Build the model o_mmcc <- QueueingModel(i_mmcc) ## Returns the Wqq Wqq(o_mmcc)
Returns the mean time spend in queue when there is queue in the M/M/c/K queueing model
## S3 method for class 'o_MMCK' Wqq(x, ...)## S3 method for class 'o_MMCK' Wqq(x, ...)
x |
a object of class o_MMCK |
... |
aditional arguments |
Returns the mean time spend in queue when there is queue in the M/M/c/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the Wqq Wqq(o_mmck)## See example 10.11 in reference [Sixto2004] for more details. ## create input parameters i_mmck <- NewInput.MMCK(lambda=8, mu=4, c=5, k=12) ## Build the model o_mmck <- QueueingModel(i_mmck) ## Returns the Wqq Wqq(o_mmck)
Returns the mean time spend in queue when there is queue in the M/M/c/K/K queueing model
## S3 method for class 'o_MMCKK' Wqq(x, ...)## S3 method for class 'o_MMCKK' Wqq(x, ...)
x |
a object of class o_MMCKK |
... |
aditional arguments |
Returns the mean time spend in queue when there is queue in the M/M/c/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the Wqq Wqq(o_mmckk)## create input parameters i_mmckk <- NewInput.MMCKK(lambda=8, mu=2, c=5, k=12, method=0) ## Build the model o_mmckk <- QueueingModel(i_mmckk) ## Returns the Wqq Wqq(o_mmckk)
Returns the mean time spend in queue when there is queue in the M/M/c/K/m queueing model
## S3 method for class 'o_MMCKM' Wqq(x, ...)## S3 method for class 'o_MMCKM' Wqq(x, ...)
x |
a object of class o_MMCKM |
... |
aditional arguments |
Returns the mean time spend in queue when there is queue in the M/M/c/K/m queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the Wqq Wqq(o_mmckm)## create input parameters i_mmckm <- NewInput.MMCKM(lambda=0.25, mu=4, c=2, k=4, m=8, method=0) ## Build the model o_mmckm <- QueueingModel(i_mmckm) ## Returns the Wqq Wqq(o_mmckm)
Returns the mean time spend in queue when there is queue in the M/M/Infinite queueing model
## S3 method for class 'o_MMInf' Wqq(x, ...)## S3 method for class 'o_MMInf' Wqq(x, ...)
x |
a object of class o_MMInf |
... |
aditional arguments |
Returns the mean time spend in queue when there is queue in the M/M/Infinite queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the Wqq Wqq(o_mminf)## create input parameters i_mminf <- NewInput.MMInf(lambda=0.25, mu=4, n=0) ## Build the model o_mminf <- QueueingModel(i_mminf) ## Returns the Wqq Wqq(o_mminf)
Returns the mean time spend in queue when there is queue in the M/M/Infinite/K/K queueing model
## S3 method for class 'o_MMInfKK' Wqq(x, ...)## S3 method for class 'o_MMInfKK' Wqq(x, ...)
x |
a object of class o_MMInfKK |
... |
aditional arguments |
Returns the mean time spend in queue when there is queue in the M/M/Infinite/K/K queueing model
[Kleinrock1975] Leonard Kleinrock (1975).
Queueing Systems Vol 1: Theory.
John Wiley & Sons.
## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the Wqq Wqq(o_MMInfKK)## create input parameters i_MMInfKK <- NewInput.MMInfKK(lambda=0.25, mu=4, k=4) ## Build the model o_MMInfKK <- QueueingModel(i_MMInfKK) ## Returns the Wqq Wqq(o_MMInfKK)
Returns the normalized mean response time in a queueing model
WWs(x, ...)WWs(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Returns the normalized mean response time in a queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the WWs WWs(o_mm1kk)## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the WWs WWs(o_mm1kk)
Returns the normalized mean response time in the M/M/1/K/K queueing model
## S3 method for class 'o_MM1KK' WWs(x, ...)## S3 method for class 'o_MM1KK' WWs(x, ...)
x |
a object of class o_MM1KK |
... |
aditional arguments |
Returns the normalized mean response time in the M/M/1/K/K queueing model
[Sixto2004] Sixto Rios Insua, Alfonso Mateos Caballero, M Concepcion Bielza Lozoya, Antonio Jimenez Martin (2004).
Investigacion Operativa. Modelos deterministicos y estocasticos.
Editorial Centro de Estudios Ramon Areces.
## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the WWs WWs(o_mm1kk)## See example 10.13 in reference [Sixto2004] for more details. ## create input parameters i_mm1kk <- NewInput.MM1KK(lambda=0.25, mu=4, k=2, method=3) ## Build the model o_mm1kk <- QueueingModel(i_mm1kk) ## Returns the WWs WWs(o_mm1kk)